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Theorem con34b 283
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b ((φψ) ↔ (¬ ψ → ¬ φ))

Proof of Theorem con34b
StepHypRef Expression
1 con3 126 . 2 ((φψ) → (¬ ψ → ¬ φ))
2 ax-3 8 . 2 ((¬ ψ → ¬ φ) → (φψ))
31, 2impbii 180 1 ((φψ) ↔ (¬ ψ → ¬ φ))
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:  mtt  329  pm4.14  561  sscon34  3661  evenodddisjlem1  4515
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