Theorem 3ad2antl1 1162

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 1157	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 981

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 983

This theorem is referenced by:  acexmid  5966  f1oen4g  6866  f1dom4g  6867  ordiso2  7163  addlocpr  7684  distrlem1prl  7730  distrlem1pru  7731  ltsopr  7744  addcanprlemu  7763  fzo1fzo0n0  10344  pfxsuffeqwrdeq  11189  prodfap0  11971  prodfrecap  11972  muldvds2  12243  dvds2add  12251  dvds2sub  12252  dvdstr  12254  qusaddvallemg  13280  mulgnnsubcl  13585  mulgpropdg  13615  ringidss  13906  lmodprop2d  14225  cnpnei  14806  upxp  14859  lgsval4lem  15603