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Mirrors > Home > MPE Home > Th. List > 3ad2antr1 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 25-Dec-2007.) |
Ref | Expression |
---|---|
3ad2antl.1 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3ad2antr1 | ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓 ∧ 𝜏)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ad2antl.1 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
2 | 1 | adantrr 714 | . 2 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓)) → 𝜃) |
3 | 2 | 3adantr3 1170 | 1 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓 ∧ 𝜏)) → 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: simpr1 1193 simpr1l 1229 simpr1r 1230 simpr11 1256 simpr12 1257 simpr13 1258 ispod 5598 funcnvqp 6613 dfwe2 7764 poxp 8117 cfcoflem 10270 axdc3lem 10448 fzadd2 13541 fzosubel2 13697 hashdifpr 14380 pfxccat3a 14693 sqrt0 15193 iscatd2 17630 funcestrcsetclem9 18105 funcsetcestrclem9 18120 curf2cl 18189 yonedalem4c 18235 grpsubadd 18948 mulgnnass 19026 mulgnn0ass 19027 dprdss 19941 dprd2da 19954 srgdilem 20087 lsssn0 20703 zntoslem 21332 sraassab 21642 psrbaglesuppOLD 21698 blsscls 24237 iimulcl 24681 pi1grplem 24797 pi1xfrf 24801 dvconst 25667 logexprlim 26961 wwlksnextbi 29412 clwwlkccatlem 29506 clwwlkccat 29507 umgr3cyclex 29700 nvss 30110 disjdsct 32188 idlsrgmnd 32899 issgon 33416 measdivcst 33517 measdivcstALTV 33518 prv1n 34717 elmrsubrn 34806 poimirlem28 36820 ftc1anc 36873 fdc 36917 cvrnbtwn3 38450 paddasslem9 39003 paddasslem17 39011 pmapjlln1 39030 lautj 39268 lautm 39269 dfsalgen2 45357 smflimlem4 45790 lidldomnnring 46918 funcringcsetcALTV2lem9 47032 funcringcsetclem9ALTV 47055 lincresunit3lem2 47250 isthincd2 47747 |
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