Theorem 3ad2antl1 1183

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
3ad2antl1	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
2	1	adantlr 477	. 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃)
3	2	3adantl2 1178	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  acexmid  6012  f1oen4g  6920  f1dom4g  6921  ordiso2  7225  addlocpr  7746  distrlem1prl  7792  distrlem1pru  7793  ltsopr  7806  addcanprlemu  7825  fzo1fzo0n0  10412  pfxsuffeqwrdeq  11269  prodfap0  12096  prodfrecap  12097  muldvds2  12368  dvds2add  12376  dvds2sub  12377  dvdstr  12379  qusaddvallemg  13406  mulgnnsubcl  13711  mulgpropdg  13741  ringidss  14032  lmodprop2d  14352  cnpnei  14933  upxp  14986  lgsval4lem  15730  clwwlkccatlem  16195  clwwlkccat  16196