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Theorem nsyl4 156
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 144 . 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  938  axc7  2128  moanim  2528  moexex  2540  nfunsn  6182  mptrcl  6246  card2on  8403  carden2a  8736  wwlksnfi  26670  ax10fromc7  33660  axc5c711  33683  axc5c711to11  33686  naecoms-o  33692  axc5c4c711  38084  axc5c4c711to11  38088  afvco2  40560
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