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Theorem jcn 162
Description: Theorem joining the consequents of two premises. Theorem 8 of [Margaris] p. 60. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Assertion
Ref Expression
jcn (𝜑 → (¬ 𝜓 → ¬ (𝜑𝜓)))

Proof of Theorem jcn
StepHypRef Expression
1 pm2.27 42 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
21con3d 152 1 (𝜑 → (¬ 𝜓 → ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  jcnd  163  jath  33658  nmotru  34583  meran1  34586  onpsstopbas  34605  bj-brrelex12ALT  35224
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