Theorem uun132p1

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	uun132p1.1	|- ( ( ( ps /\ ch ) /\ ph ) -> th )
Assertion	uun132p1	|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		uun132p1.1	|- ( ( ( ps /\ ch ) /\ ph ) -> th )
2		3anass	|- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		ancom	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
4	2 3	bitri	|- ( ( ph /\ ps /\ ch ) <-> ( ( ps /\ ch ) /\ ph ) )
5	4 1	sylbi	|- ( ( ph /\ ps /\ ch ) -> th )