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Theorem pm5.74ri 249
Description: Distribution of implication over biconditional (reverse inference rule). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74ri.1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )
Assertion
Ref Expression
pm5.74ri  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem pm5.74ri
StepHypRef Expression
1 pm5.74ri.1 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )
2 pm5.74 247 . 2  |-  ( (
ph  ->  ( ps  <->  ch )
)  <->  ( ( ph  ->  ps )  <->  ( ph  ->  ch ) ) )
31, 2mpbir 212 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188
This theorem is referenced by:  bitrd  256  bibi2d  319  tbt  345  cbval2  2092  sbied  2214  sbco2d  2221  axgroth6  9204  isprm2  14575  ufileu  20876  bj-cbval2v  31243
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