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Theorem nsyli 156
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 149 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
41, 3syl5 34 1 (𝜑 → (𝜃 → ¬ 𝜓))
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:  necon3ad  2950  tz7.7  5934  onssneli  6017  tz7.48-2  7741  tz7.49  7744  php  8351  nndomo  8361  elirrv  8708  setind  8825  zorn2lem3  9573  alephval2  9647  inar1  9850  dfon2lem6  32068  sltres  32191  finminlem  32688  onint1  32819  poimirlem4  33769  gneispace  39038
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