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Theorem pm5.74i 169
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 pm5.74 168 . 2 ((φ → (ψχ)) ↔ ((φψ) ↔ (φχ)))
31, 2mpbi 133 1 ((φψ) ↔ (φχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bitrd  177  imbi2i  215  bibi2d  221  ibib  234  ibibr  235  anclb  302  pm5.42  303  ancrb  305  equsalh  1596  equsal  1597  sb6a  1846  ralbiia  2316  raaan  3306
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