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Theorem nsyli 155
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 148 . 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  2803  tz7.7  5708  onssneli  5796  tz7.48-2  7482  tz7.49  7485  php  8088  nndomo  8098  elirrv  8448  setind  8554  zorn2lem3  9264  alephval2  9338  inar1  9541  dfon2lem6  31394  sltres  31518  finminlem  31954  onint1  32090  poimirlem4  33045  gneispace  37914
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