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Theorem con2bid 319
Description: A contraposition deduction. (Contributed by NM, 15-Apr-1995.)
Hypothesis
Ref Expression
con2bid.1 (φ → (ψ ↔ ¬ χ))
Assertion
Ref Expression
con2bid (φ → (χ ↔ ¬ ψ))

Proof of Theorem con2bid
StepHypRef Expression
1 con2bid.1 . 2 (φ → (ψ ↔ ¬ χ))
2 con2bi 318 . 2 ((χ ↔ ¬ ψ) ↔ (ψ ↔ ¬ χ))
31, 2sylibr 203 1 (φ → (χ ↔ ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176
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
This theorem is referenced by:  con1bid  320  necon2abid  2573  necon2bbid  2574  r19.9rzv  3644  iotanul  4354
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