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Theorem pm5.74i 178
Description: Distribution of implication over biconditional (inference rule). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74i.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
pm5.74i ((𝜑𝜓) ↔ (𝜑𝜒))

Proof of Theorem pm5.74i
StepHypRef Expression
1 pm5.74i.1 . 2 (𝜑 → (𝜓𝜒))
2 pm5.74 177 . 2 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) ↔ (𝜑𝜒)))
31, 2mpbi 143 1 ((𝜑𝜓) ↔ (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bitrd  186  imbi2i  224  bibi2d  230  ibib  243  ibibr  244  anclb  312  pm5.42  313  ancrb  315  equsalh  1655  equsal  1656  sb6a  1906  ralbiia  2381  raaan  3355  isprm4  10645
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