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Theorem exbir 1341
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
StepHypRef Expression
1 bi2 125 . . 3  |-  ( ( ch  <->  th )  ->  ( th  ->  ch ) )
21imim2i 12 . 2  |-  ( ( ( ph  /\  ps )  ->  ( ch  <->  th )
)  ->  ( ( ph  /\  ps )  -> 
( th  ->  ch ) ) )
32expd 249 1  |-  ( ( ( ph  /\  ps )  ->  ( ch  <->  th )
)  ->  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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