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Theorem pm5.32ri 448
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 447 . 2  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ch )
)
3 ancom 264 . 2  |-  ( ( ps  /\  ph )  <->  (
ph  /\  ps )
)
4 ancom 264 . 2  |-  ( ( ch  /\  ph )  <->  (
ph  /\  ch )
)
52, 3, 43bitr4i 211 1  |-  ( ( ps  /\  ph )  <->  ( ch  /\  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anbi1i  451  pm5.36  582  pm5.61  766  oranabs  787  ceqsralt  2685  ceqsrexbv  2788  reuind  2860  rabsn  3558  dfoprab2  5784  xpsnen  6681  nn1suc  8696  isprm2  11694  isxms2  12516
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