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Theorem pm5.74ri 263
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 pm5.74 261 . 2 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) ↔ (𝜑𝜒)))
31, 2mpbir 222 1 (𝜑 → (𝜓𝜒))
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:  bitrd  270  bibi2d  333  tbt  360  cbval2  2452  cbvaldva  2454  sbied  2570  sbco2d  2577  axgroth6  9932  isprm2  15609  ufileu  21932  bj-cbval2v  33048
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