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Theorem jc 590
Description: Inference joining the consequents of two premises. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jc.1 (𝜑𝜓)
jc.2 (𝜑𝜒)
Assertion
Ref Expression
jc (𝜑 → ¬ (𝜓 → ¬ 𝜒))

Proof of Theorem jc
StepHypRef Expression
1 jc.1 . 2 (𝜑𝜓)
2 jc.2 . 2 (𝜑𝜒)
3 pm3.2im 576 . 2 (𝜓 → (𝜒 → ¬ (𝜓 → ¬ 𝜒)))
41, 2, 3sylc 60 1 (𝜑 → ¬ (𝜓 → ¬ 𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 554  ax-in2 555
This theorem is referenced by: (None)
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