Theorem ad2ant2lr 728

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 23-Nov-2007.)

Hypothesis

Ref	Expression
ad2ant2.1	⊢ ((φ ∧ ψ) → χ)

Assertion

Ref	Expression
ad2ant2lr	⊢ (((θ ∧ φ) ∧ (ψ ∧ τ)) → χ)

Proof of Theorem ad2ant2lr

Step	Hyp	Ref	Expression
1		ad2ant2.1	. . 3 ⊢ ((φ ∧ ψ) → χ)
2	1	adantrr 697	. 2 ⊢ ((φ ∧ (ψ ∧ τ)) → χ)
3	2	adantll 694	1 ⊢ (((θ ∧ φ) ∧ (ψ ∧ τ)) → χ)

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  caovmo  5646  nchoicelem19  6308