Theorem 3impdirp1 39043

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. Commuted version of 3impdir 1382. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
3impdirp1	|- ( ( ph /\ ch /\ ps ) -> th )

Proof of Theorem 3impdirp1

Step	Hyp	Ref	Expression
1		ancom 466	. . 3 |- ( ( ( ch /\ ps ) /\ ( ph /\ ps ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )
2		3impdirp1.1	. . 3 |- ( ( ( ch /\ ps ) /\ ( ph /\ ps ) ) -> th )
3	1, 2	sylbir 225	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ps ) ) -> th )
4	3	3impdir 1382	1 |- ( ( ph /\ ch /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)