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Theorem pm5.74ri 259
Description: Distribution of implication over biconditional (reverse inference rule). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74ri.1 ((𝜑𝜓) ↔ (𝜑𝜒))
Assertion
Ref Expression
pm5.74ri (𝜑 → (𝜓𝜒))

Proof of Theorem pm5.74ri
StepHypRef Expression
1 pm5.74ri.1 . 2 ((𝜑𝜓) ↔ (𝜑𝜒))
2 pm5.74 257 . 2 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) ↔ (𝜑𝜒)))
31, 2mpbir 219 1 (𝜑 → (𝜓𝜒))
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:  bitrd  266  bibi2d  330  tbt  357  cbval2  2266  cbvaldva  2268  sbied  2396  sbco2d  2403  axgroth6  9506  isprm2  15181  ufileu  21480  bj-cbval2v  31717
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