![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > ioorp | Structured version Unicode version |
Description: The set of positive reals expressed as an open interval. (Contributed by Steve Rodriguez, 25-Nov-2007.) |
Ref | Expression |
---|---|
ioorp |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ioopos 11473 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | df-rp 11093 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | eqtr4i 2483 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 ax-cnex 9439 ax-resscn 9440 ax-1cn 9441 ax-icn 9442 ax-addcl 9443 ax-addrcl 9444 ax-mulcl 9445 ax-mulrcl 9446 ax-i2m1 9451 ax-1ne0 9452 ax-rnegex 9454 ax-rrecex 9455 ax-cnre 9456 ax-pre-lttri 9457 ax-pre-lttrn 9458 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-nel 2647 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-iun 4271 df-br 4391 df-opab 4449 df-mpt 4450 df-id 4734 df-po 4739 df-so 4740 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-ov 6193 df-oprab 6194 df-mpt2 6195 df-1st 6677 df-2nd 6678 df-er 7201 df-en 7411 df-dom 7412 df-sdom 7413 df-pnf 9521 df-mnf 9522 df-xr 9523 df-ltxr 9524 df-le 9525 df-rp 11093 df-ioo 11405 |
This theorem is referenced by: rpsup 11806 advlog 22215 advlogexp 22216 logccv 22224 cxpcn3 22302 loglesqr 22312 rlimcnp 22475 rlimcnp2 22476 divsqrsumlem 22489 amgmlem 22499 logfacbnd3 22678 logexprlim 22680 dchrisum0lem2a 22882 logdivsum 22898 log2sumbnd 22909 elxrge02 26241 xrge0iifcnv 26497 xrge0iifiso 26499 xrge0iifhom 26501 xrge0mulc1cn 26505 esumdivc 26666 signsply0 27086 itg2gt0cn 28585 dvasin 28618 |
Copyright terms: Public domain | W3C validator |