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Theorem pm5.74d 171
Description: Distribution of implication over biconditional (deduction rule). (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 pm5.74 168 . 2 ((ψ → (χθ)) ↔ ((ψχ) ↔ (ψθ)))
31, 2sylib 127 1 (φ → ((ψχ) ↔ (ψθ)))
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:  imbi2d  219  imim21b  241  pm5.74da  417  cbval2  1793  dfiin2g  3681  brecop  6132  dom2lem  6188  nn0ind-raph  8131
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