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Theorem pm4.53r 815
Description: One direction of theorem *4.53 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)
Assertion
Ref Expression
pm4.53r ((¬ 𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem pm4.53r
StepHypRef Expression
1 pm4.52im 814 . 2 ((𝜑 ∧ ¬ 𝜓) → ¬ (¬ 𝜑𝜓))
21con2i 567 1 ((¬ 𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 101  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  undif3ss  3226
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