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Theorem con3dimp 597
Description: Variant of con3d 594 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
con3dimp.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
con3dimp ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

Proof of Theorem con3dimp
StepHypRef Expression
1 con3dimp.1 . . 3 (𝜑 → (𝜓𝜒))
21con3d 594 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
32imp 122 1 ((𝜑 ∧ ¬ 𝜒) → ¬ 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:  nelneq  2183  nelneq2  2184  bcpasc  9842  fiinfnf1o  9862
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