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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 6138 frfi 9288 wemappo 9544 iccsplit 13462 ccatswrd 14618 sqrmo 15198 pcdvdstr 16809 vdwlem12 16925 mreexexlem4d 17591 iscatd2 17625 oppccomfpropd 17673 resssetc 18042 resscatc 18059 mod1ile 18446 mod2ile 18447 prdssgrpd 18624 prdsmndd 18658 grprcan 18858 prdsringd 20134 lmodprop2d 20534 lssintcl 20575 prdslmodd 20580 islmhm2 20649 islbs3 20768 ofco2 21953 mdetmul 22125 restopnb 22679 regsep2 22880 iunconn 22932 blsscls2 24013 met2ndci 24031 xrsblre 24327 nosupbnd1lem5 27215 conway 27300 addsass 27488 mulscom 27595 legso 27850 colline 27900 tglowdim2ln 27902 cgrahl 28078 f1otrg 28122 f1otrge 28123 ax5seglem4 28190 ax5seglem5 28191 axcontlem4 28225 axcontlem8 28229 axcontlem9 28230 axcontlem10 28231 eengtrkg 28244 rusgrnumwwlks 29228 frgr3v 29528 submomnd 32228 ogrpaddltbi 32236 erdszelem8 34189 elmrsubrn 34511 btwncomim 34985 btwnswapid 34989 broutsideof3 35098 outsideoftr 35101 outsidele 35104 isbasisrelowllem1 36236 isbasisrelowllem2 36237 cvrletrN 38143 ltltncvr 38294 atcvrj2b 38303 2at0mat0 38396 paddasslem11 38701 pmod1i 38719 lautcvr 38963 tendoplass 39654 tendodi1 39655 tendodi2 39656 cdlemk34 39781 mendassa 41936 grumnud 43045 3adantlr3 43724 ssinc 43776 ssdec 43777 ioondisj2 44206 ioondisj1 44207 subsubelfzo0 46034 prdsrngd 46677 ply1mulgsumlem2 47068 lincresunit3lem2 47161 catprs 47631 |
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