Theorem ancomd

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

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

Proof

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