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Theorem nsyld 132
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 125 . 2 (φ → (¬ χ → ¬ τ))
41, 3syld 40 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  166  sbn  2062  enprmaplem3  6078  nnc3n3p1  6278
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