Theorem ad2ant2l 726

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

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

Assertion

Ref	Expression
ad2ant2l	⊢ (((θ ∧ φ) ∧ (τ ∧ ψ)) → χ)

Proof of Theorem ad2ant2l

Step	Hyp	Ref	Expression
1		ad2ant2.1	. . 3 ⊢ ((φ ∧ ψ) → χ)
2	1	adantrl 696	. 2 ⊢ ((φ ∧ (τ ∧ ψ)) → χ)
3	2	adantll 694	1 ⊢ (((θ ∧ φ) ∧ (τ ∧ ψ)) → 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:  tfin11  4493  ce0addcnnul  6179  nchoicelem19  6307