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Theorem pm5.32ri 436
Description: Distribution of implication over biconditional (inference rule). (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 435 . 2  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ch )
)
3 ancom 257 . 2  |-  ( ( ps  /\  ph )  <->  (
ph  /\  ps )
)
4 ancom 257 . 2  |-  ( ( ch  /\  ph )  <->  (
ph  /\  ch )
)
52, 3, 43bitr4i 205 1  |-  ( ( ps  /\  ph )  <->  ( ch  /\  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anbi1i  439  pm5.36  552  pm5.61  718  oranabs  739  ceqsralt  2598  ceqsrexbv  2698  reuind  2767  rabsn  3465  dfoprab2  5580  xpsnen  6326  nn1suc  8009
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