Theorem com3rgbi 38720

Description: The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The completed Virtual Deduction Proof (not shown) was minimized. The minimized proof is shown. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

1::	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )
2::	|- ( ( ph -> ( ch -> ( ps -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) )
3:1,2:	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) )
4::	|- ( ( ch -> ( ph -> ( ps -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )
5::	|- ( ( ph -> ( ch -> ( ps -> th ) ) ) -> ( ph -> ( ps -> ( ch -> th ) ) ) )
6:4,5:	|- ( ( ch -> ( ph -> ( ps -> th ) ) ) -> ( ph -> ( ps -> ( ch -> th ) ) ) )
qed:3,6:	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) <-> ( ch -> ( ph -> ( ps -> th ) ) ) )

Assertion

Ref	Expression
com3rgbi	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) <-> ( ch -> ( ph -> ( ps -> th ) ) ) )

Proof of Theorem com3rgbi

Step	Hyp	Ref	Expression
1		pm2.04 90	. . 3 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ph -> ( ch -> th ) ) ) )
2	1	com24 95	. 2 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) )
3		pm2.04 90	. . 3 |- ( ( ch -> ( ph -> ( ps -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )
4	3	com34 91	. 2 |- ( ( ch -> ( ph -> ( ps -> th ) ) ) -> ( ph -> ( ps -> ( ch -> th ) ) ) )
5	2, 4	impbii 199	1 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) <-> ( ch -> ( ph -> ( ps -> th ) ) ) )

Syntax hints:   -> wi 4   <-> wb 196

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

This theorem is referenced by:  impexpdcom  38721