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Theorem nsyld 154
Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
nsyld.1 (𝜑 → (𝜓 → ¬ 𝜒))
nsyld.2 (𝜑 → (𝜏𝜒))
Assertion
Ref Expression
nsyld (𝜑 → (𝜓 → ¬ 𝜏))

Proof of Theorem nsyld
StepHypRef Expression
1 nsyld.1 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
2 nsyld.2 . . 3 (𝜑 → (𝜏𝜒))
32con3d 148 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜏))
41, 3syld 47 1 (𝜑 → (𝜓 → ¬ 𝜏))
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:  pm2.65d  187  pltn2lp  16909  alexsubALTlem4  21794  eupth2eucrct  26977  ifeqeqx  29249  cvrat  34227  radcnvrat  38034
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