Theorem ancom1s

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	an32s.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	ancom1s	|- ( ( ( ps /\ ph ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		an32s.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
2		pm3.22	|- ( ( ps /\ ph ) -> ( ph /\ ps ) )
3	2 1	sylan	|- ( ( ( ps /\ ph ) /\ ch ) -> th )