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Theorem con3dimp 624
Description: Variant of con3d 620 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 620 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
32imp 123 1 ((𝜑 ∧ ¬ 𝜒) → ¬ 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:  nelneq  2240  nelneq2  2241  nelss  3158  nnnninf  7023  bcpasc  10519  fiinfnf1o  10539
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