Theorem ad2antlr 707

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.) (Proof shortened by Wolf Lammen, 20-Nov-2012.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad2antlr	⊢ (((χ ∧ φ) ∧ θ) → ψ)

Proof of Theorem ad2antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	adantr 451	. 2 ⊢ ((φ ∧ θ) → ψ)
3	2	adantll 694	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:  ad3antlr  711  simplr  731  simplrl  736  simplrr  737  ax11eq  2193  ax11el  2194  ltfinirr  4458  sfintfin  4533  caovord3  5632  nntccl  6171  sbthlem3  6206  nchoicelem17  6306