Theorem uun111

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	uun111.1	|- ( ( ph /\ ph /\ ph ) -> ps )
Assertion	uun111	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		uun111.1	|- ( ( ph /\ ph /\ ph ) -> ps )
2		3anass	|- ( ( ph /\ ph /\ ph ) <-> ( ph /\ ( ph /\ ph ) ) )
3		anabs5	|- ( ( ph /\ ( ph /\ ph ) ) <-> ( ph /\ ph ) )
4		anidm	|- ( ( ph /\ ph ) <-> ph )
5	2 3 4	3bitri	|- ( ( ph /\ ph /\ ph ) <-> ph )
6	5 1	sylbir	|- ( ph -> ps )