Theorem uun2131p1

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	uun2131p1.1	|- ( ( ( ph /\ ch ) /\ ( ph /\ ps ) ) -> th )
Assertion	uun2131p1	|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		uun2131p1.1	|- ( ( ( ph /\ ch ) /\ ( ph /\ ps ) ) -> th )
2		ancom	|- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) ) <-> ( ( ph /\ ch ) /\ ( ph /\ ps ) ) )
3	2 1	sylbi	|- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) ) -> th )
4	3	3impdi	|- ( ( ph /\ ps /\ ch ) -> th )