Theorem 3ad2antl3 1068

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 445	. 2 ⊢ (((𝜏 ∧ 𝜑) ∧ 𝜒) → 𝜃)
3	2	3adantl1 1060	1 ⊢ (((𝜓 ∧ 𝜏 ∧ 𝜑) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  rspc3ev  2666  brcogw  4504  cocan1  5427  ov6g  5638  prarloclemarch2  6517  ltpopr  6693  ltsopr  6694  zdivmul  8330