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Theorem pm5.32ri 455
Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 12-Mar-1995.)
Hypothesis
Ref Expression
pm5.32i.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
pm5.32ri  |-  ( ( ps  /\  ph )  <->  ( ch  /\  ph )
)

Proof of Theorem pm5.32ri
StepHypRef Expression
1 pm5.32i.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21pm5.32i 454 . 2  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ch )
)
3 ancom 266 . 2  |-  ( ( ps  /\  ph )  <->  (
ph  /\  ps )
)
4 ancom 266 . 2  |-  ( ( ch  /\  ph )  <->  (
ph  /\  ch )
)
52, 3, 43bitr4i 212 1  |-  ( ( ps  /\  ph )  <->  ( ch  /\  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  anbi1i  458  pm5.36  610  pm5.61  794  oranabs  815  ceqsralt  2764  ceqsrexbv  2868  reuind  2942  rabsn  3659  dfoprab2  5921  xpsnen  6820  nn1suc  8937  isprm2  12116  ismnd  12819  dfgrp2e  12902  isxms2  13922
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