| Metamath Proof Explorer |
This is the GIF version. Change to Unicode version | |
| Symbol | ASCII |
| ( | |
| ) | |
| | -> |
| -. | |
| wff | |
| |- | |
| ph | |
| ps | |
| ch | |
| th | |
| ta | |
| et | |
| ze | |
| si | |
| rh | |
| | <-> |
| | \/ |
| | /\ |
| | -/\ |
| | T. |
| | F. |
| A. | |
| set | |
| x | |
| y | |
| z | |
| w | |
| v | |
| u | |
| | = |
| class | |
| A | |
| B | |
| | e. |
| E. | |
| [ | |
| | / |
| ] | |
| f | |
| g | |
| E! | |
| E* | |
| t | |
| { | |
| | | |
| } | |
| C | |
| D | |
| P | |
| Q | |
| R | |
| S | |
| T | |
| U | |
| e | |
| h | |
| i | |
| j | |
| k | |
| m | |
| n | |
| o | |
| E | |
| F | |
| G | |
| H | |
| I | |
| J | |
| K | |
| L | |
| M | |
| N | |
| V | |
| W | |
| X | |
| Y | |
| Z | |
| O | |
| s | |
| r | |
| q | |
| p | |
| a | |
| b | |
| c | |
| d | |
| l | l |
| | =/= |
| | e/ |
| _V | |
| [_ | |
| ]_ | |
| | \ |
| | u. |
| | i^i |
| | C_ |
| | C. |
| (/) | |
| if | |
| , | |
| ~P | |
| <. | |
| >. | |
| U. | |
| |^| | |
| U_ | |
| |^|_ | |
| Tr | |
| _E | |
| _I | |
| | Po |
| | Or |
| | Fr |
| | We |
| Ord | |
| On | |
| Lim | |
| suc | |
| om | |
| | X. |
| `' | |
| dom | |
| ran | |
| | |` |
| " | |
| | o. |
| Rel | |
| Fun | |
| | Fn |
| : | |
| --> | |
| -1-1-> | |
| -onto-> | |
| -1-1-onto-> | |
| ` | |
| | Isom |
| | |-> |
| 1st | |
| 2nd | |
| iota | |
| rec | |
| 1o | |
| 2o | |
| | +o |
| | .o |
| | ^o |
| Er | |
| /. | |
| | ^m |
| | ^pm |
| X_ | |
| | ~~ |
| | ~<_ |
| | ~< |
| Fin | |
| Undef | Undef |
| iota_ | |
| sup | |
| R1 | |
| rank | |
| card | |
| aleph | |
| cf | |
| | +c |
| N. | |
| | +N |
| | .N |
| | <N |
| | +pQ |
| | .pQ |
| | ~Q |
| Q. | |
| 1Q | |
| | +Q |
| | .Q |
| *Q | |
| | <Q |
| P. | |
| 1P | |
| | +P. |
| | .P. |
| | <P |
| | +pR |
| | .pR |
| | ~R |
| R. | |
| 0R | |
| 1R | |
| -1R | |
| | +R |
| | .R |
| | <R |
| | <RR |
| CC | |
| RR | |
| 0 | |
| 1 | |
| _i | |
| | + |
| | x. |
| | - |
| -u | |
| | <_ |
| NN | |
| NN0 | |
| ZZ | |
| RR+ | |
| | +oo |
| | -oo |
| RR* | |
| | < |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| |_ | |
| | mod |
| | == |
| (,) | (,) |
| (,] | (,] |
| [,) | [,) |
| [,] | [,] |
| ZZ>= | |
| ... | |
| | seq1 |
| | shift |
| limsup | |
| | seq |
| | seq0 |
| ^ | |
| sqr | |
| Re | |
| Im | |
| * | |
| abs | |
| ! | |
| | _C |
| # | # |
| | ~~> |
| sum_ | |
| -cn-> | |
| exp | |
| _e | |
| sin | |
| cos | |
| pi | |
| Top | Top |
| TopSp | TopSp |
| Bases | Bases |
| topGen | topGen |
| | tX |
| int | int |
| cls | cls |
| Clsd | Clsd |
| nei | nei |
| limPt | limPt |
| Cn | Cn |
| CnP | CnP |
| Haus | Haus |
| Met | Met |
| MetSp | MetSp |
| ball | ball |
| Open | Open |
| ~~>m | |
| Cau | Cau |
| CMet | CMet |
| Grp | Grp |
| Id | Id |
| inv | inv |
| | /g |
| ^g | |
| Abel | Abel |
| SubGrp | SubGrp |
| GrpAct | GrpAct |
| Ring | Ring |
| DivRing | DivRing |
| *-Fld | *-Fld |
| CVec | CVec |
| NrmCVec | NrmCVec |
| +v | |
| BaseSet | BaseSet |
| .s | |
| 0v | |
| -v | |
| norm | |
| IndMet | IndMet |
| .i | |
| SubSp | SubSp |
| LnOp | LnOp |
| normOp | normOp |
| BLnOp | BLnOp |
| | 0op |
| adj | adj |
| HmOp | HmOp |
| CPreHil | CPreHil |
| CBan | CBan |
| CHil | CHil |
| Poset | Poset |
| supw | supw |
| infw | infw |
| Lat | Lat |
| log | |
| GrpHom | GrpHom |
| GrpIso | GrpIso |
| SymGrp | SymGrp |
| Toset | Toset |
| fi | fi |
| Homeo | Homeo |
| ~= | ~= |
| subSp | subSp |
| fBas | fBas |
| filGen | filGen |
| Fil | Fil |
| fLim1 | fLim1 |
| FilMap | FilMap |
| fLimf | fLimf |
| Comp | Comp |
| Fre | Fre |
| Con | Con |
| Plig | Plig |
| Dir | Dir |
| tail | tail |
| Ass | Ass |
| ExId | ExId |
| Magma | Magma |
| SemiGrp | SemiGrp |
| Mnd | Mnd |
| Com2 | Com2 |
| Fld | Fld |
| ~H | |
| | +h |
| | .h |
| 0h | |
| | -h |
| | .ih |
| normh | |
| Cauchy | |
| | ~~>v |
| SH | |
| CH | |
| _|_ | |
| | +H |
| span | |
| | vH |
| | \/H |
| 0H | |
| | C_H |
| proj | proj |
| 0hop | 0hop |
| | Iop |
| | +op |
| | .op |
| | -op |
| | +fn |
| | .fn |
| normop | normop |
| ConOp | ConOp |
| LinOp | LinOp |
| BndLinOp | BndLinOp |
| UniOp | UniOp |
| HrmOp | HrmOp |
| normfn | normfn |
| null | null |
| ConFn | ConFn |
| LinFn | LinFn |
| adjh | adjh |
| bra | bra |
| ketbra | ketbra |
| | <_op |
| eigvec | eigvec |
| eigval | eigval |
| Lambda | |
| States | |
| CHStates | CHStates |
| Atoms | |
| | <o |
| | MH |
| | MH* |
| ph' | |
| ps' | |
| ch' | |
| th' | |
| ta' | |
| et' | |
| ze' | |
| si' | |
| rh' | |
| ph" | |
| ps" | |
| ch" | |
| th" | |
| ta" | |
| et" | |
| ze" | |
| si" | |
| rh" | |
| ph0 | |
| ps0 | |
| ch0_ | |
| th0 | |
| ta0 | |
| et0 | |
| ze0 | |
| si0 | |
| rh0 | |
| ph1 | |
| ps1 | |
| ch1 | |
| th1 | |
| ta1 | |
| et1 | |
| ze1 | |
| si1 | |
| rh1 | |
| a' | |
| b' | |
| c' | |
| d' | |
| e' | |
| f' | |
| g' | |
| h' | |
| i' | |
| j' | |
| k' | |
| l' | |
| m' | |
| n' | |
| o' | |
| p' | |
| q' | |
| r' | |
| s' | |
| t' | |
| u' | |
| v' | |
| w' | |
| x' | |
| y' | |
| z' | |
| a" | |
| b" | |
| c" | |
| d" | |
| e" | |
| f" | |
| g" | |
| h" | |
| i" | |
| j" | |
| k" | |
| l" | |
| m" | |
| n" | |
| o" | |
| p" | |
| q" | |
| r" | |
| s" | |
| t" | |
| u" | |
| v" | |
| w" | |
| x" | |
| y" | |
| z" | |
| a0 | |
| b0 | |
| c0_ | |
| d0 | |
| e0 | |
| f0_ | |
| g0 | |
| h0 | |
| i0 | |
| j0 | |
| k0 | |
| l0 | |
| m0 | |
| n0_ | |
| o0 | |
| p0 | |
| q0 | |
| r0 | |
| s0 | |
| t0 | |
| u0 | |
| v0 | |
| w0 | |
| x0 | |
| y0 | |
| z0 | |
| a1 | |
| b1 | |
| c1_ | |
| d1 | |
| e1 | |
| f1 | |
| g1 | |
| h1 | |
| i1 | |
| j1 | |
| k1 | |
| l1 | |
| m1 | |
| n1 | |
| o1 | |
| p1 | |
| q1 | |
| r1 | |
| s1 | |
| t1 | |
| u1 | |
| v1 | |
| w1 | |
| x1 | |
| y1 | |
| z1 | |
| A' | |
| B' | |
| C' | |
| D' | |
| E' | |
| F' | |
| G' | |
| H' | |
| I' | |
| J' | |
| K' | |
| L' | |
| M' | |
| N' | |
| O' | |
| P' | |
| Q' | |
| R' | |
| S' | |
| T' | |
| U' | |
| V' | |
| W' | |
| X' | |
| Y' | |
| Z' | |
| A" | |
| B" | |
| C" | |
| D" | |
| E" | |
| F" | |
| G" | |
| H" | |
| I" | |
| J" | |
| K" | |
| L" | |
| M" | |
| N" | |
| O" | |
| P" | |
| Q" | |
| R" | |
| S" | |
| T" | |
| U" | |
| V" | |
| W" | |
| X" | |
| Y" | |
| Z" | |
| A0 | |
| B0 | |
| C0 | |
| D0 | |
| E0 | |
| F0 | |
| G0 | |
| H0 | |
| I0 | |
| J0 | |
| K0 | |
| L0 | |
| M0 | |
| N0 | |
| O0 | |
| P0 | |
| Q0 | |
| R0 | |
| S0 | |
| T0 | |
| U0 | |
| V0 | |
| W0 | |
| X0 | |
| Y0 | |
| Z0 | |
| A1_ | |
| B1_ | |
| C1_ | |
| D1_ | |
| E1 | |
| F1_ | |
| G1_ | |
| H1_ | |
| I1_ | |
| J1 | |
| K1 | |
| L1_ | |
| M1_ | |
| N1 | |
| O1_ | |
| P1 | |
| Q1 | |
| R1_ | |
| S1_ | |
| T1 | |
| U1 | |
| V1_ | |
| W1 | |
| X1 | |
| Y1 | |
| Z1 | |
| fns | _fns |
| pred | _pred |
| Se | _Se |
| FrSe | _FrSe |
| trCl | _trCl |
| TrFo | _TrFo |
| || | |
| | gcd |
| Prime | Prime |
| Pred | Pred |
| Trcl | Trcl |
| No | No |
| <s | <s |
| bday | bday |
| gcdOLD | gcdOLD |
| A1 | A1 |
| A2 | A2 |
| B1 | B1 |
| B2 | B2 |
| C1 | C1 |
| C2 | C2 |
| D1 | D1 |
| D2 | D2 |
| F1 | F1 |
| F2 | F2 |
| G1 | G1 |
| G2 | G2 |
| H1 | H1 |
| H2 | H2 |
| I1 | I1 |
| I2 | I2 |
| L1 | L1 |
| L2 | L2 |
| M1 | M1 |
| M2 | M2 |
| O1 | O1 |
| O2 | O2 |
| Ro1 | Ro1 |
| Ro2 | Ro2 |
| S1 | S1 |
| S2 | S2 |
| V1 | V1 |
| V2 | V2 |
| V3 | V3 |
| +t | +t |
| -t | -t |
| .t | .t |
| ~t | ~t |
| 0t | 0t |
| 1t | 1t |
| +w | +w |
| -w | -w |
| .w | .w |
| 0w | 0w |
| ~w | ~w |
| (+) | |
| [.] | |
| <> | |
| () | |
| until | until |
| t+ | t+ |
| t* | t* |
| pr | pr |
| pr | prj |
| cset | cset |
| LatAlg | LatAlg |
| cur1 | cur1 |
| cur2 | cur2 |
| mxl | mxl |
| mnl | mnl |
| ub | ub |
| lb | lb |
| Preset | Preset |
| ge | ge |
| se | se |
| AntiDir | AntiDir |
| OrHom | OrHom |
| DecFun | DecFun |
| OrIso | OrIso |
| prod3 | prod3_ |
| prod_ | |
| Com1 | Com1 |
| Free | Free |
| star | star |
| ^md | ^md |
| Str | Str |
| Strx | Strx |
| len | len |
| conc | conc |
| str | str |
| Tofld | Tofld |
| zeroDiv | zeroDiv |
| Vec | Vec |
| SubVec | SubVec |
| RVec | RVec |
| +m | +m |
| xm | xm |
| .m | .m |
| RAffSp | RAffSp |
| topX | topX |
| TopGrp | TopGrp |
| Dgra | Dgra |
| Alg | Alg |
| dom | dom_ |
| cod | cod_ |
| id | id_ |
| o | o_ |
| Ded | Ded |
| Cat | Cat |
| hom | hom |
| Epi | Epi |
| Monic | Monic |
| Iso | Iso |
| cinv | cinv |
| Func | Func |
| Isofunc | Isofunc |
| SubCat | SubCat |
| Tarski | Tarski |
| tarskiMap | tarskiMap |
| tar | tar |
| tr | tr |
| Uni | Uni |
| line | line |
| Plibg | Plibg |
| Plibg0 | Plibg0 |
| Plibg1 | Plibg1 |
| Plibg2 | Plibg2 |
| Plibg3 | Plibg3 |
| Plibg4a | Plibg4a |
| Plibg4b | Plibg4b |
| seg | seg |
| 1stc | |
| 2ndc | |
| Fne | Fne |
| Ref | Ref |
| PtFin | PtFin |
| LocFin | LocFin |
| Kol2 | Kol2 |
| Reg | Reg |
| Nrm | Nrm |
| UFil | UFil |
| fClus | fClus |
| fClusf | fClusf |
| II | |
| ~~>t | |
| TotBnd | TotBnd |
| Bnd | Bnd |
| Ismty | Ismty |
| Rn | |
| PHtpy | PHtpy |
| ~=ph | |
| pi1b | |
| *p | |
| pi1 | |
| RngHom | RngHom |
| RngIso | RngIso |
| ~=r | |
| CRing | CRing |
| Idl | Idl |
| PrIdl | PrIdl |
| MaxIdl | MaxIdl |
| PrRing | PrRing |
| Dmn | Dmn |
| IdlGen | IdlGen |
| Prt | Prt |
| HypGrph | HypGrph |
| PsGrph | PsGrph |
| SmpGrph | SmpGrph |
| Smo | Smo |
| . | (. |
| . | ). |
| ⊢ | |-. |
| Struct | Struct |
| StrBldr | StrBldr |
| base | base |
| le | le |
| PosetNEW | PosetNEW |
| lt | lt |
| geNEW | geNEW |
| gt | gt |
| lub | lub |
| glb | glb |
| join | join |
| meet | meet |
| 1. | 1. |
| 0. | 0. |
| LatNEW | LatNEW |
| ComplLat | ComplLat |
| oc | oc |
| OP | OP |
| cm | cm |
| OL | OL |
| OML | OML |
| | <oNEW |
| AtomsNEW | AtomsNEW |
| AtLat | AtLat |
| HL | HL |
| +g | +g |
| GrpNEW | GrpNEW |
| 0g | 0g |
| -g | -g |
| AbelNEW | AbelNEW |
| .r | .r |
| RingNEW | RingNEW |
| 1rNEW | 1rNEW |
| DivRingNEW | DivRingNEW |
| invr | invr |
| *v | *v |
| Ring* | Ring* |
| DivRing* | DivRing* |
| vbase | vbase |
| vadd | vadd |
| vsca | vsca |
| LVec | LVec |
| 0vNEW | 0vNEW |
| ip | ip |
| PreHil | PreHil |
| +ss | +ss |
| ocv | ocv |
| CSubSp | CSubSp |
| Hil | Hil |
| Lines | Lines |
| Points | Points |
| PSubSp | PSubSp |
| pmap | pmap |
| +P | +P |
| _|_P | _|_P |