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Mirrors > Home > MPE Home > Th. List > simplr1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
Ref | Expression |
---|---|
simplr1 | ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 1134 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
2 | 1 | ad2antlr 723 | 1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∧ w3a 1085 |
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 206 df-an 395 df-3an 1087 |
This theorem is referenced by: soltmin 6136 frfi 9290 wemappo 9546 iccsplit 13466 ccatswrd 14622 sqrmo 15202 pcdvdstr 16813 vdwlem12 16929 mreexexlem4d 17595 iscatd2 17629 oppccomfpropd 17677 resssetc 18046 resscatc 18063 mod1ile 18450 mod2ile 18451 prdssgrpd 18658 prdsmndd 18692 grprcan 18894 prdsrngd 20070 prdsringd 20209 lmodprop2d 20678 lssintcl 20719 prdslmodd 20724 islmhm2 20793 islbs3 20913 ofco2 22173 mdetmul 22345 restopnb 22899 regsep2 23100 iunconn 23152 blsscls2 24233 met2ndci 24251 xrsblre 24547 nosupbnd1lem5 27451 conway 27537 addsass 27727 mulscom 27834 legso 28117 colline 28167 tglowdim2ln 28169 cgrahl 28345 f1otrg 28389 f1otrge 28390 ax5seglem4 28457 ax5seglem5 28458 axcontlem4 28492 axcontlem8 28496 axcontlem9 28497 axcontlem10 28498 eengtrkg 28511 rusgrnumwwlks 29495 frgr3v 29795 lmhmimasvsca 32467 submomnd 32498 ogrpaddltbi 32506 erdszelem8 34487 elmrsubrn 34809 btwncomim 35289 btwnswapid 35293 broutsideof3 35402 outsideoftr 35405 outsidele 35408 isbasisrelowllem1 36539 isbasisrelowllem2 36540 cvrletrN 38446 ltltncvr 38597 atcvrj2b 38606 2at0mat0 38699 paddasslem11 39004 pmod1i 39022 lautcvr 39266 tendoplass 39957 tendodi1 39958 tendodi2 39959 cdlemk34 40084 mendassa 42238 grumnud 43347 3adantlr3 44026 ssinc 44077 ssdec 44078 ioondisj2 44504 ioondisj1 44505 subsubelfzo0 46332 ply1mulgsumlem2 47155 lincresunit3lem2 47248 catprs 47718 |
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