Theorem anabss5 789

Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)

Hypothesis

Ref	Expression
anabss5.1	⊢ ((φ ∧ (φ ∧ ψ)) → χ)

Assertion

Ref	Expression
anabss5	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabss5

Step	Hyp	Ref	Expression
1		anabss5.1	. . 3 ⊢ ((φ ∧ (φ ∧ ψ)) → χ)
2	1	anassrs 629	. 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:  anabsi5  790