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Theorem jc 139
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 137 . 2 (ψ → (χ → ¬ (ψ → ¬ χ)))
41, 2, 3sylc 56 1 (φ → ¬ (ψ → ¬ χ))
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: (None)
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