Theorem un2122 39017

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 3-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
un2122.1	|- ( ( ( ph /\ ps ) /\ ps /\ ps ) -> ch )

Assertion

Ref	Expression
un2122	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem un2122

Step	Hyp	Ref	Expression
1		3anass 1042	. . 3 |- ( ( ( ph /\ ps ) /\ ps /\ ps ) <-> ( ( ph /\ ps ) /\ ( ps /\ ps ) ) )
2		anandir 872	. . . 4 |- ( ( ( ph /\ ps ) /\ ps ) <-> ( ( ph /\ ps ) /\ ( ps /\ ps ) ) )
3		ancom 466	. . . . 5 |- ( ( ( ph /\ ps ) /\ ps ) <-> ( ps /\ ( ph /\ ps ) ) )
4		anabs7 852	. . . . 5 |- ( ( ps /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )
5	3, 4	bitri 264	. . . 4 |- ( ( ( ph /\ ps ) /\ ps ) <-> ( ph /\ ps ) )
6	2, 5	bitr3i 266	. . 3 |- ( ( ( ph /\ ps ) /\ ( ps /\ ps ) ) <-> ( ph /\ ps ) )
7	1, 6	bitri 264	. 2 |- ( ( ( ph /\ ps ) /\ ps /\ ps ) <-> ( ph /\ ps ) )
8		un2122.1	. 2 |- ( ( ( ph /\ ps ) /\ ps /\ ps ) -> ch )
9	7, 8	sylbir 225	1 |- ( ( ph /\ ps ) -> ch )

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:  suctrALT3  39160