Theorem 3ad2antl3 1161

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

Hypothesis

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

Assertion

Ref	Expression
3ad2antl3	⊢ (((𝜓 ∧ 𝜏 ∧ 𝜑) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl3

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
2	1	adantll 476	. 2 ⊢ (((𝜏 ∧ 𝜑) ∧ 𝜒) → 𝜃)
3	2	3adantl1 1153	1 ⊢ (((𝜓 ∧ 𝜏 ∧ 𝜑) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 978

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 980

This theorem is referenced by:  rspc3ev  2860  brcogw  4798  cocan1  5790  ov6g  6014  prarloclemarch2  7420  ltpopr  7596  ltsopr  7597  zdivmul  9345  lcmdvds  12081