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Theorem exp4a 358
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4a.1  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
Assertion
Ref Expression
exp4a  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp4a
StepHypRef Expression
1 exp4a.1 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
2 impexp 259 . 2  |-  ( ( ( ch  /\  th )  ->  ta )  <->  ( ch  ->  ( th  ->  ta ) ) )
31, 2syl6ib 159 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  exp4b  359  exp4d  361  exp45  366  exp5c  368  tfri3  6124  nnmordi  6265  fiintim  6629  ndvdssub  11195
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