Theorem anabsan 786

Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem anabsan

Step	Hyp	Ref	Expression
1		pm4.24 624	. 2 ⊢ (φ ↔ (φ ∧ φ))
2		anabsan.1	. 2 ⊢ (((φ ∧ φ) ∧ ψ) → χ)
3	1, 2	sylanb 458	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:  anabss1  787  anabss5  789  anandis  803