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Theorem nsyl3 615
Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.)
Hypotheses
Ref Expression
nsyl3.1 (𝜑 → ¬ 𝜓)
nsyl3.2 (𝜒𝜓)
Assertion
Ref Expression
nsyl3 (𝜒 → ¬ 𝜑)

Proof of Theorem nsyl3
StepHypRef Expression
1 nsyl3.2 . 2 (𝜒𝜓)
2 nsyl3.1 . . 3 (𝜑 → ¬ 𝜓)
32a1i 9 . 2 (𝜒 → (𝜑 → ¬ 𝜓))
41, 3mt2d 614 1 (𝜒 → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 603  ax-in2 604
This theorem is referenced by:  con2i  616  nsyl  617  pm2.65i  628  cesare  2103  cesaro  2107  pwnss  4083  sucprcreg  4464  reg3exmidlemwe  4493  reldmtpos  6150  snexxph  6838  elfi2  6860  ismkvnex  7029  fzn  9829  seq3f1olemqsum  10280
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