Theorem uun123

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	uun123.1	|- ( ( ph /\ ch /\ ps ) -> th )
Assertion	uun123	|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		uun123.1	|- ( ( ph /\ ch /\ ps ) -> th )
2		3ancomb	|- ( ( ph /\ ch /\ ps ) <-> ( ph /\ ps /\ ch ) )
3	2 1	sylbir	|- ( ( ph /\ ps /\ ch ) -> th )