Theorem expcomdg 38706

Description: Biconditional form of expcomd 454. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.)

Assertion

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

Proof of Theorem expcomdg

Step	Hyp	Ref	Expression
1		ancomst 468	. . 3 |- ( ( ( ps /\ ch ) -> th ) <-> ( ( ch /\ ps ) -> th ) )
2		impexp 462	. . 3 |- ( ( ( ch /\ ps ) -> th ) <-> ( ch -> ( ps -> th ) ) )
3	1, 2	bitri 264	. 2 |- ( ( ( ps /\ ch ) -> th ) <-> ( ch -> ( ps -> th ) ) )
4	3	imbi2i 326	1 |- ( ( ph -> ( ( ps /\ ch ) -> th ) ) <-> ( ph -> ( ch -> ( ps -> th ) ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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

This theorem is referenced by: (None)