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  6006  f1oen4g  6911  f1dom4g  6912  ordiso2  7213  addlocpr  7734  distrlem1prl  7780  distrlem1pru  7781  ltsopr  7794  addcanprlemu  7813  fzo1fzo0n0  10395  pfxsuffeqwrdeq  11245  prodfap0  12071  prodfrecap  12072  muldvds2  12343  dvds2add  12351  dvds2sub  12352  dvdstr  12354  qusaddvallemg  13381  mulgnnsubcl  13686  mulgpropdg  13716  ringidss  14007  lmodprop2d  14327  cnpnei  14908  upxp  14961  lgsval4lem  15705  clwwlkccatlem  16137  clwwlkccat  16138