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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 1137 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
2 | 1 | ad2antlr 726 | 1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 ∧ w3a 1088 |
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 398 df-3an 1090 |
This theorem is referenced by: soltmin 6135 frfi 9285 wemappo 9541 iccsplit 13459 ccatswrd 14615 sqrmo 15195 pcdvdstr 16806 vdwlem12 16922 mreexexlem4d 17588 iscatd2 17622 oppccomfpropd 17670 resssetc 18039 resscatc 18056 mod1ile 18443 mod2ile 18444 prdssgrpd 18621 prdsmndd 18655 grprcan 18855 prdsringd 20128 lmodprop2d 20527 lssintcl 20568 prdslmodd 20573 islmhm2 20642 islbs3 20761 ofco2 21945 mdetmul 22117 restopnb 22671 regsep2 22872 iunconn 22924 blsscls2 24005 met2ndci 24023 xrsblre 24319 nosupbnd1lem5 27205 conway 27290 addsass 27478 mulscom 27585 legso 27840 colline 27890 tglowdim2ln 27892 cgrahl 28068 f1otrg 28112 f1otrge 28113 ax5seglem4 28180 ax5seglem5 28181 axcontlem4 28215 axcontlem8 28219 axcontlem9 28220 axcontlem10 28221 eengtrkg 28234 rusgrnumwwlks 29218 frgr3v 29518 submomnd 32216 ogrpaddltbi 32224 erdszelem8 34178 elmrsubrn 34500 btwncomim 34974 btwnswapid 34978 broutsideof3 35087 outsideoftr 35090 outsidele 35093 isbasisrelowllem1 36225 isbasisrelowllem2 36226 cvrletrN 38132 ltltncvr 38283 atcvrj2b 38292 2at0mat0 38385 paddasslem11 38690 pmod1i 38708 lautcvr 38952 tendoplass 39643 tendodi1 39644 tendodi2 39645 cdlemk34 39770 mendassa 41922 grumnud 43031 3adantlr3 43710 ssinc 43762 ssdec 43763 ioondisj2 44193 ioondisj1 44194 subsubelfzo0 46021 prdsrngd 46664 ply1mulgsumlem2 47022 lincresunit3lem2 47115 catprs 47585 |
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