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Theorem pm5.32da 622
 Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 9-Dec-2006.)
Hypothesis
Ref Expression
pm5.32da.1 ((φ ψ) → (χθ))
Assertion
Ref Expression
pm5.32da (φ → ((ψ χ) ↔ (ψ θ)))

Proof of Theorem pm5.32da
StepHypRef Expression
1 pm5.32da.1 . . 3 ((φ ψ) → (χθ))
21ex 423 . 2 (φ → (ψ → (χθ)))
32pm5.32d 620 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-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  rexbida  2629  reubida  2793  rmobida  2798  fcnvres  5243  funbrfv2b  5362  dffn5  5363  fnrnfv  5364  fniniseg  5371  eqfnfv2  5393  funiunfv  5467  dff13  5471  mpteq12f  5655  mpt2eq3dva  5669  ltlenlec  6207
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