Theorem anabss1 787

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Hypothesis

Ref	Expression
anabss1.1	⊢ (((φ ∧ ψ) ∧ φ) → χ)

Assertion

Ref	Expression
anabss1	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabss1

Step	Hyp	Ref	Expression
1		anabss1.1	. . 3 ⊢ (((φ ∧ ψ) ∧ φ) → χ)
2	1	an32s 779	. 2 ⊢ (((φ ∧ φ) ∧ ψ) → χ)
3	2	anabsan 786	1 ⊢ ((φ ∧ 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:  anabss4  788