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Theorem imanim 677
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 874. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim ((𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem imanim
StepHypRef Expression
1 annimim 675 . 2 ((𝜑 ∧ ¬ 𝜓) → ¬ (𝜑𝜓))
21con2i 616 1 ((𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-in1 603  ax-in2 604
This theorem is referenced by:  difdif  3201  ssdif0im  3427  inssdif0im  3430  nominpos  8971
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