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Mirrors > Home > MPE Home > Th. List > ad2ant2rl | Structured version Visualization version GIF version |
Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 24-Nov-2007.) |
Ref | Expression |
---|---|
ad2ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ad2ant2rl | ⊢ (((𝜑 ∧ 𝜃) ∧ (𝜏 ∧ 𝜓)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | adantrl 716 | . 2 ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓)) → 𝜒) |
3 | 2 | adantlr 715 | 1 ⊢ (((𝜑 ∧ 𝜃) ∧ (𝜏 ∧ 𝜓)) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
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 207 df-an 396 |
This theorem is referenced by: poseq 8182 omwordri 8609 omxpenlem 9112 infxpabs 10249 domfin4 10349 isf32lem7 10397 ordpipq 10980 muladd 11693 lemul12b 12122 mulge0b 12136 qaddcl 13005 iooshf 13463 elfzomelpfzo 13807 expnegz 14134 swrdccatin1 14760 bitsshft 16509 setscom 17214 lubun 18573 grplmulf1o 19044 grpraddf1o 19045 srhmsubc 20697 lmodfopne 20915 lidl1el 21254 frlmipval 21817 en2top 23008 cnpnei 23288 kgenidm 23571 ufileu 23943 fmfnfmlem4 23981 isngp4 24641 fsumcn 24908 evth 25005 cmslssbn 25420 mbfmulc2lem 25696 itg1addlem4 25748 itg1addlem4OLD 25749 dgreq0 26320 cxplt3 26757 cxple3 26758 basellem4 27142 sltsolem1 27735 nodenselem7 27750 zmulscld 28398 axcontlem2 28995 umgr2edg 29241 nbumgrvtx 29378 clwwlkf1 30078 umgrhashecclwwlk 30107 frgrncvvdeqlem9 30336 frgrwopreglem5ALT 30351 numclwwlk7lem 30418 grpoidinvlem3 30535 grpoideu 30538 grporcan 30547 3oalem2 31692 hmops 32049 adjadd 32122 mdslmd4i 32362 mdexchi 32364 mdsymlem1 32432 bnj607 34909 cvxsconn 35228 tailfb 36360 lindsadd 37600 poimirlem14 37621 mblfinlem4 37647 ismblfin 37648 ismtyres 37795 ghomco 37878 rngoisocnv 37968 1idl 38013 ps-2 39461 cfsetsnfsetf1 47009 usgrgrtrirex 47853 grlictr 47911 gpgvtx0 47944 srhmsubcALTV 48169 aacllem 49032 |
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