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Theorem pm5.74d 247
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)
Hypothesis
Ref Expression
pm5.74d.1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Assertion
Ref Expression
pm5.74d  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )

Proof of Theorem pm5.74d
StepHypRef Expression
1 pm5.74d.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
2 pm5.74 244 . 2  |-  ( ( ps  ->  ( ch  <->  th ) )  <->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
31, 2sylib 196 1  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
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 185
This theorem is referenced by:  imbi2d  316  imim21b  367  pm5.74da  687  cbval2  1975  dvelimdf  2027  sbied  2102  dfiin2g  4202  oneqmini  4769  tfindsg  6470  findsg  6502  brecop  7192  dom2lem  7348  indpi  9075  uzindOLD  10735  nn0ind-raph  10741  cncls2  18876  ismbl2  21009  voliunlem3  21032  mdbr2  25699  dmdbr2  25706  mdsl2i  25725  mdsl2bi  25726  sgn3da  26923  wl-dral1d  28358  wl-equsald  28366  ralbidar  29699  bj-cbval2v  32236  cvlsupr3  32987  cdleme32fva  34079  cdlemk33N  34551  cdlemk34  34552
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