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Theorem exbiri 606
Description: Inference form of exbir 1371. This proof is exbiriVD 28308 automatically translated and minimized. (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 472 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ch )
32exp31 588 1  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359
This theorem is referenced by:  biimp3ar  1284  eqrdav  2387  tfrlem9  6583  sbthlem1  7154  addcanpr  8857  axpre-sup  8978  lbreu  9891  zmax  10504  ucnima  18233  usgraidx2vlem2  21278  mdslmd1lem1  23677  mdslmd1lem2  23678  dfon2  25173  cgrextend  25657  brsegle  25757  brabg2  26109
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
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