Theorem exbir 1285

Description: Exportation implication also converting head from biconditional to conditional. This proof is exbirVD 16677 automatically translated and minimized. (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 166	. . 3 |- ((ch <-> th) -> (th -> ch))
2	1	imim2i 11	. 2 |- (((ph /\ ps) -> (ch <-> th)) -> ((ph /\ ps) -> (th -> ch)))
3	2	exp3a 405	1 |- (((ph /\ ps) -> (ch <-> th)) -> (ph -> (ps -> (th -> ch))))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

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