Theorem uun132p1 39013

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.)

Hypothesis

Ref	Expression
uun132p1.1	|- ( ( ( ps /\ ch ) /\ ph ) -> th )

Assertion

Ref	Expression
uun132p1	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem uun132p1

Step	Hyp	Ref	Expression
1		3anass 1042	. . 3 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		ancom 466	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) /\ ph ) )
3	1, 2	bitri 264	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ps /\ ch ) /\ ph ) )
4		uun132p1.1	. 2 |- ( ( ( ps /\ ch ) /\ ph ) -> th )
5	3, 4	sylbi 207	1 |- ( ( ph /\ ps /\ ch ) -> 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)