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Theorem nsyli 588
Description: A negated syllogism inference. (Contributed by NM, 3-May-1994.)
Hypotheses
Ref Expression
nsyli.1 (𝜑 → (𝜓𝜒))
nsyli.2 (𝜃 → ¬ 𝜒)
Assertion
Ref Expression
nsyli (𝜑 → (𝜃 → ¬ 𝜓))

Proof of Theorem nsyli
StepHypRef Expression
1 nsyli.2 . 2 (𝜃 → ¬ 𝜒)
2 nsyli.1 . . 3 (𝜑 → (𝜓𝜒))
32con3d 571 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
41, 3syl5 32 1 (𝜑 → (𝜃 → ¬ 𝜓))
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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