Theorem anabsi7 792

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsi7.1	⊢ (ψ → ((φ ∧ ψ) → χ))

Assertion

Ref	Expression
anabsi7	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi7

Step	Hyp	Ref	Expression
1		anabsi7.1	. . 3 ⊢ (ψ → ((φ ∧ ψ) → χ))
2	1	anabsi6 791	. 2 ⊢ ((ψ ∧ φ) → χ)
3	2	ancoms 439	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:  elunii  3897