Theorem 3ad2antl1 1186

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 1181	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1005

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 1007

This theorem is referenced by:  acexmid  6027  f1oen4g  6968  f1dom4g  6969  ordiso2  7277  addlocpr  7799  distrlem1prl  7845  distrlem1pru  7846  ltsopr  7859  addcanprlemu  7878  fzo1fzo0n0  10468  pfxsuffeqwrdeq  11328  prodfap0  12169  prodfrecap  12170  muldvds2  12441  dvds2add  12449  dvds2sub  12450  dvdstr  12452  qusaddvallemg  13479  mulgnnsubcl  13784  mulgpropdg  13814  ringidss  14106  lmodprop2d  14427  cnpnei  15013  upxp  15066  lgsval4lem  15813  clwwlkccatlem  16324  clwwlkccat  16325