Theorem ad2antrl 708

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad2antrl	⊢ ((χ ∧ (φ ∧ θ)) → ψ)

Proof of Theorem ad2antrl

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	adantr 451	. 2 ⊢ ((φ ∧ θ) → ψ)
3	2	adantl 452	1 ⊢ ((χ ∧ (φ ∧ θ)) → ψ)

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:  simprl  732  simprll  738  simprlr  739  preaddccan2  4456  ncfinlower  4484  tfinnn  4535  sfinltfin  4536  enadjlem1  6060  sbthlem3  6206  nchoicelem17  6306  nchoice  6309