Theorem anabsi6 791

Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000.)

Hypothesis

Ref	Expression
anabsi6.1	⊢ (φ → ((ψ ∧ φ) → χ))

Assertion

Ref	Expression
anabsi6	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi6

Step	Hyp	Ref	Expression
1		anabsi6.1	. . 3 ⊢ (φ → ((ψ ∧ φ) → χ))
2	1	ancomsd 440	. 2 ⊢ (φ → ((φ ∧ ψ) → χ))
3	2	anabsi5 790	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:  anabsi7  792