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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  2028  dvelimdf  2078  sbied  2152  dfiin2g  4365  oneqmini  4938  tfindsg  6694  findsg  6726  brecop  7422  dom2lem  7574  indpi  9302  uzindOLD  10978  nn0ind-raph  10985  cncls2  19900  ismbl2  22063  voliunlem3  22087  mdbr2  27341  dmdbr2  27348  mdsl2i  27367  mdsl2bi  27368  sgn3da  28655  wl-dral1d  30146  wl-equsald  30154  ralbidar  31516  bj-cbval2v  34403  cvlsupr3  35170  cdleme32fva  36264  cdlemk33N  36736  cdlemk34  36737
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