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Theorem pm5.74d 264
Description: Distribution of implication over biconditional (deduction form). (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 pm5.74 261 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) ↔ (𝜓𝜃)))
31, 2sylib 209 1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 197
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 198
This theorem is referenced by:  imbi2d  331  imim21b  383  pm5.74da  838  cbval2  2382  cbvaldva  2384  dvelimdf  2429  sbied  2500  dfiin2g  4709  oneqmini  5959  tfindsg  7258  findsg  7291  brecop  8043  dom2lem  8200  indpi  9982  nn0ind-raph  11724  cncls2  21357  ismbl2  23585  voliunlem3  23610  mdbr2  29611  dmdbr2  29618  mdsl2i  29637  mdsl2bi  29638  sgn3da  31051  bj-cbval2v  33171  wl-dral1d  33743  wl-equsald  33750  cvlsupr3  35300  cdleme32fva  36393  cdlemk33N  36865  cdlemk34  36866  ralbidar  39321  tfis2d  43096
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