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Theorem exbiri 374
Description: Inference form of exbir 1368. (Contributed by Alan Sare, 31-Dec-2011.) (Proof shortened by Wolf Lammen, 27-Jan-2013.)
Hypothesis
Ref Expression
exbiri.1  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
Assertion
Ref Expression
exbiri  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )

Proof of Theorem exbiri
StepHypRef Expression
1 exbiri.1 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
21biimpar 291 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ch )
32exp31 356 1  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
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:  biimp3ar  1280  eqrdav  2084  tfrlem9  6040  sbthlem1  6613  lbreu  8344  uzsubsubfz  9396  elfzodifsumelfzo  9543
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