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Mirrors > Home > MPE Home > Th. List > ancli | Structured version Visualization version GIF version |
Description: Deduction conjoining antecedent to left of consequent. (Contributed by NM, 12-Aug-1993.) |
Ref | Expression |
---|---|
ancli.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ancli | ⊢ (𝜑 → (𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝜑 → 𝜑) | |
2 | ancli.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | jca 553 | 1 ⊢ (𝜑 → (𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: pm4.45im 583 barbari 2555 cesaro 2561 camestros 2562 calemos 2572 swopo 4969 xpdifid 5481 xpima 5495 elrnrexdm 6271 ixpsnf1o 7834 php4 8032 ssnnfi 8064 inf3lem6 8413 rankuni 8609 cardprclem 8688 nqpr 9715 letrp1 10744 p1le 10745 sup2 10858 peano2uz2 11341 uzind 11345 uzid 11578 qreccl 11684 xrsupsslem 12009 supxrunb1 12021 faclbnd4lem4 12945 cshweqdifid 13417 fprodsplit1f 14560 idghm 17498 efgred 17984 srgbinom 18368 subrgid 18605 lmodfopne 18724 m1detdiag 20222 1elcpmat 20339 phtpcer 22602 phtpcerOLD 22603 pntrlog2bndlem2 25067 wlkon 26061 trlon 26070 pthon 26105 spthon 26112 constr3lem6 26177 clwwlkf 26322 hvpncan 27280 chsupsn 27656 ssjo 27690 elim2ifim 28748 rrhre 29393 pmeasadd 29714 bnj596 30070 bnj1209 30121 bnj996 30279 bnj1110 30304 bnj1189 30331 arg-ax 31585 bj-mo3OLD 32022 unirep 32677 rp-isfinite6 36883 clsk1indlem2 37360 ntrclsss 37381 clsneiel1 37426 monoords 38452 fsumsplit1 38639 fmul01 38647 fmuldfeqlem1 38649 fmuldfeq 38650 fmul01lt1lem1 38651 icccncfext 38773 iblspltprt 38865 stoweidlem3 38896 stoweidlem17 38910 stoweidlem19 38912 stoweidlem20 38913 stoweidlem23 38916 stirlinglem15 38981 fourierdlem16 39016 fourierdlem21 39021 fourierdlem72 39071 fourierdlem89 39088 fourierdlem90 39089 fourierdlem91 39090 hoidmvlelem4 39488 salpreimalegt 39597 zeoALTV 40119 n0rex 40310 1wlkres 40879 clwwlksf 41222 0pthon-av 41295 c0mgm 41699 c0mhm 41700 2zrngnmrid 41740 mndpsuppss 41946 linc0scn0 42006 |
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