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Theorem nsyl4 157
Description: A negated syllogism inference. (Contributed by NM, 15-Feb-1996.)
Hypotheses
Ref Expression
nsyl4.1 (𝜑𝜓)
nsyl4.2 𝜑𝜒)
Assertion
Ref Expression
nsyl4 𝜒𝜓)

Proof of Theorem nsyl4
StepHypRef Expression
1 nsyl4.2 . . 3 𝜑𝜒)
21con1i 146 . 2 𝜒𝜑)
3 nsyl4.1 . 2 (𝜑𝜓)
42, 3syl 17 1 𝜒𝜓)
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:  pm5.55  962  axc7  2310  moanim  2693  moexex  2705  nfunsn  6442  mptrcl  6507  card2on  8695  carden2a  9072  wwlksnfi  27039  ax10fromc7  34671  axc5c711  34694  axc5c711to11  34697  naecoms-o  34703  axc5c4c711  39098  axc5c4c711to11  39102  afvco2  41762
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