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Theorem pm5.74d 260
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)
Hypothesis
Ref Expression
pm5.74d.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
pm5.74d (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))

Proof of Theorem pm5.74d
StepHypRef Expression
1 pm5.74d.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 pm5.74 257 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) ↔ (𝜓𝜃)))
31, 2sylib 206 1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194
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 195
This theorem is referenced by:  imbi2d  328  imim21b  380  pm5.74da  718  cbval2  2260  cbvaldva  2262  dvelimdf  2317  sbied  2391  dfiin2g  4478  oneqmini  5674  tfindsg  6924  findsg  6957  brecop  7699  dom2lem  7853  indpi  9580  nn0ind-raph  11304  cncls2  20824  ismbl2  23014  voliunlem3  23039  mdbr2  28340  dmdbr2  28347  mdsl2i  28366  mdsl2bi  28367  sgn3da  29731  bj-cbval2v  31725  wl-dral1d  32295  wl-equsald  32302  cvlsupr3  33447  cdleme32fva  34541  cdlemk33N  35013  cdlemk34  35014  ralbidar  37468
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