Theorem ad2ant2rl 729

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 24-Nov-2007.)

Hypothesis

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

Assertion

Ref	Expression
ad2ant2rl	⊢ (((φ ∧ θ) ∧ (τ ∧ ψ)) → χ)

Proof of Theorem ad2ant2rl

Step	Hyp	Ref	Expression
1		ad2ant2.1	. . 3 ⊢ ((φ ∧ ψ) → χ)
2	1	adantrl 696	. 2 ⊢ ((φ ∧ (τ ∧ ψ)) → χ)
3	2	adantlr 695	1 ⊢ (((φ ∧ θ) ∧ (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:  caovmo  5646  fnfullfunlem2  5858  spacind  6288