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Theorem jcn 624
Description: Inference joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
jcn.1 (𝜑𝜓)
jcn.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
jcn (𝜑 → ¬ (𝜓𝜒))

Proof of Theorem jcn
StepHypRef Expression
1 jcn.1 . . 3 (𝜑𝜓)
2 jcn.2 . . 3 (𝜑 → ¬ 𝜒)
31, 2jc 623 . 2 (𝜑 → ¬ (𝜓 → ¬ ¬ 𝜒))
4 notnot 601 . . 3 (𝜒 → ¬ ¬ 𝜒)
54imim2i 12 . 2 ((𝜓𝜒) → (𝜓 → ¬ ¬ 𝜒))
63, 5nsyl 600 1 (𝜑 → ¬ (𝜓𝜒))
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 586  ax-in2 587
This theorem is referenced by: (None)
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