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Theorem exp5c 373
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5c.1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ( th  /\  ta )  ->  et ) ) )
Assertion
Ref Expression
exp5c  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5c
StepHypRef Expression
1 exp5c.1 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ( th  /\  ta )  ->  et ) ) )
21exp4a 363 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( th 
->  ( ta  ->  et ) ) ) )
32expd 256 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  fiintim  6785
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