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Theorem pm5.32d 620
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 29-Oct-1996.)
Hypothesis
Ref Expression
pm5.32d.1 (φ → (ψ → (χθ)))
Assertion
Ref Expression
pm5.32d (φ → ((ψ χ) ↔ (ψ θ)))

Proof of Theorem pm5.32d
StepHypRef Expression
1 pm5.32d.1 . 2 (φ → (ψ → (χθ)))
2 pm5.32 617 . 2 ((ψ → (χθ)) ↔ ((ψ χ) ↔ (ψ θ)))
31, 2sylib 188 1 (φ → ((ψ χ) ↔ (ψ θ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  pm5.32rd  621  pm5.32da  622  anbi2d  684  cbval2  2004  cbvex2  2005  cores  5084  isoini  5497  mpt2eq123  5661  nmembers1lem3  6270
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