MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exbiri Unicode version

Theorem exbiri 605
Description: Inference form of exbir 1355. This proof is exbiriVD 28946 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 471 . 2  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ch )
32exp31 587 1  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  biimp3ar  1282  eqrdav  2295  tfrlem9  6417  sbthlem1  6987  addcanpr  8686  axpre-sup  8807  lbreu  9720  zmax  10329  mdslmd1lem1  22921  mdslmd1lem2  22922  dfon2  24219  cgrextend  24703  brsegle  24803  isder  25810  sgplpte21d  26239  brabg2  26469
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 177  df-an 360
  Copyright terms: Public domain W3C validator