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Mirrors > Home > ILE Home > Th. List > nsyl3 | GIF version |
Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.) |
Ref | Expression |
---|---|
nsyl3.1 | ⊢ (𝜑 → ¬ 𝜓) |
nsyl3.2 | ⊢ (𝜒 → 𝜓) |
Ref | Expression |
---|---|
nsyl3 | ⊢ (𝜒 → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nsyl3.2 | . 2 ⊢ (𝜒 → 𝜓) | |
2 | nsyl3.1 | . . 3 ⊢ (𝜑 → ¬ 𝜓) | |
3 | 2 | a1i 9 | . 2 ⊢ (𝜒 → (𝜑 → ¬ 𝜓)) |
4 | 1, 3 | mt2d 625 | 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 614 ax-in2 615 |
This theorem is referenced by: con2i 627 nsyl 628 pm2.65i 639 cesare 2130 cesaro 2134 pwnss 4159 sucprcreg 4548 reg3exmidlemwe 4578 reldmtpos 6253 snexxph 6948 elfi2 6970 ismkvnex 7152 fzn 10041 seq3f1olemqsum 10499 pcmpt2 12341 |
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