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Theorem imanim 821
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 822. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim ((𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem imanim
StepHypRef Expression
1 annimim 818 . 2 ((𝜑 ∧ ¬ 𝜓) → ¬ (𝜑𝜓))
21con2i 590 1 ((𝜑𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-in1 577  ax-in2 578
This theorem is referenced by:  difdif  3111  ssdif0im  3332  inssdif0im  3335  nominpos  8563
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