Theorem ancomd 438

Description: Commutation of conjuncts in consequent. (Contributed by Jeff Hankins, 14-Aug-2009.)

Hypothesis

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

Assertion

Ref	Expression
ancomd	⊢ (φ → (χ ∧ ψ))

Proof of Theorem ancomd

Step	Hyp	Ref	Expression
1		ancomd.1	. 2 ⊢ (φ → (ψ ∧ χ))
2		ancom 437	. 2 ⊢ ((ψ ∧ χ) ↔ (χ ∧ ψ))
3	1, 2	sylib 188	1 ⊢ (φ → (χ ∧ ψ))

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:  simprd  449  2reu5  3045  brcnv  4893