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Mirrors > Home > MPE Home > Th. List > 3ad2antl2 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.) |
Ref | Expression |
---|---|
3ad2antl.1 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3ad2antl2 | ⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ad2antl.1 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
2 | 1 | adantlr 712 | . 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
3 | 2 | 3adantl1 1165 | 1 ⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
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 396 df-3an 1088 |
This theorem is referenced by: simpl2 1191 simpl2l 1225 simpl2r 1226 simpl21 1250 simpl22 1251 simpl23 1252 fcofo 7289 cocan1 7292 ordiso2 9514 fin1a2lem9 10407 fin1a2lem12 10410 gchpwdom 10669 winainflem 10692 bpolydif 16004 dvdsmodexp 16210 muldvds1 16229 lcmdvds 16550 ramcl 16967 oddvdsnn0 19454 ghmplusg 19756 frlmsslss2 21550 frlmsslsp 21571 islindf4 21613 mamures 22113 matepmcl 22185 matepm2cl 22186 pmatcollpw2lem 22500 cnpnei 22989 ssref 23237 qtopss 23440 elfm2 23673 flffbas 23720 cnpfcf 23766 deg1ldg 25846 brbtwn2 28431 colinearalg 28436 axsegconlem1 28443 upgrpredgv 28667 cusgrrusgr 29106 upgrewlkle2 29131 wwlksm1edg 29403 clwwlkf 29568 wwlksext2clwwlk 29578 nvmul0or 30171 hoadddi 31324 volfiniune 33527 bnj548 34207 funsseq 35044 nn0prpwlem 35511 fnemeet1 35555 curfv 36772 lindsadd 36785 keridl 37204 pmapglbx 38944 elpaddn0 38975 paddasslem9 39003 paddasslem10 39004 cdleme42mgN 39663 factwoffsmonot 41330 relexpxpmin 42771 ntrclsk3 43124 n0p 44032 wessf1ornlem 44183 infxr 44376 lptre2pt 44655 dvnprodlem1 44961 fourierdlem42 45164 fourierdlem48 45169 fourierdlem54 45175 fourierdlem77 45198 sge0rpcpnf 45436 hoicvr 45563 smflimsuplem7 45841 isomgrsym 46803 |
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