Theorem exbir 1325

Description: Exportation implication also converting head from biconditional to conditional. (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		bi2 121	. . 3 |- ( ( ch <-> th ) -> ( th -> ch ) )
2	1	imim2i 12	. 2 |- ( ( ( ph /\ ps ) -> ( ch <-> th ) ) -> ( ( ph /\ ps ) -> ( th -> ch ) ) )
3	2	expd 245	1 |- ( ( ( ph /\ ps ) -> ( ch <-> th ) ) -> ( ph -> ( ps -> ( th -> ch ) ) ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)