Theorem ancomsimp 1369

Description: Closed form of ancoms 439. Derived automatically from ancomsimpVD in set.mm. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
ancomsimp	⊢ (((φ ∧ ψ) → χ) ↔ ((ψ ∧ φ) → χ))

Proof of Theorem ancomsimp

Step	Hyp	Ref	Expression
1		ancom 437	. 2 ⊢ ((φ ∧ ψ) ↔ (ψ ∧ φ))
2	1	imbi1i 315	1 ⊢ (((φ ∧ ψ) → χ) ↔ ((ψ ∧ φ) → χ))

Syntax hints:   → wi 4   ↔ wb 176   ∧ 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:  exp3acom23g  1371  ralcomf  2769