Theorem 3ad2antl2 1101

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

Hypothesis

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

Assertion

Ref	Expression
3ad2antl2	⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl2

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
2	1	adantlr 460	. 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃)
3	2	3adantl1 1094	1 ⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  fcofo  5444  cocan1  5447  acexmid  5531  caovimo  5714  ordiso2  6446  ltpopr  6785  ltsopr  6786  addcanprleml  6804  addcanprlemu  6805  aptiprlemu  6830  muldvds1  10220  lcmdvds  10461