Theorem exbir 38684

Description: Exportation implication also converting the consequent from a biconditional to an implication. Derived automatically from exbirVD 39088. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

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

Proof of Theorem exbir

Step	Hyp	Ref	Expression
1		biimpr 210	. . 3 |- ( ( ch <-> th ) -> ( th -> ch ) )
2	1	imim2i 16	. 2 |- ( ( ( ph /\ ps ) -> ( ch <-> th ) ) -> ( ( ph /\ ps ) -> ( th -> ch ) ) )
3	2	expd 452	1 |- ( ( ( ph /\ ps ) -> ( ch <-> th ) ) -> ( ph -> ( ps -> ( th -> ch ) ) ) )

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)