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Theorem pm4.52im 802
Description: One direction of theorem *4.52 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)
Assertion
Ref Expression
pm4.52im ((φ ¬ ψ) → ¬ (¬ φ ψ))

Proof of Theorem pm4.52im
StepHypRef Expression
1 annimim 781 . 2 ((φ ¬ ψ) → ¬ (φψ))
2 imorr 796 . 2 ((¬ φ ψ) → (φψ))
31, 2nsyl 558 1 ((φ ¬ ψ) → ¬ (¬ φ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.53r  803
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