Theorem 3impdirp1

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. Commuted version of 3impdir . (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	3impdirp1.1	|- ( ( ( ch /\ ps ) /\ ( ph /\ ps ) ) -> th )
Assertion	3impdirp1	|- ( ( ph /\ ch /\ ps ) -> th )

Proof

Step	Hyp	Ref	Expression
1		3impdirp1.1	|- ( ( ( ch /\ ps ) /\ ( ph /\ ps ) ) -> th )
2		ancom	|- ( ( ( ch /\ ps ) /\ ( ph /\ ps ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )
3	2 1	sylbir	|- ( ( ( ph /\ ps ) /\ ( ch /\ ps ) ) -> th )
4	3	3impdir	|- ( ( ph /\ ch /\ ps ) -> th )