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Mirrors > Home > ILE Home > Th. List > mt2d | GIF version |
Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.) |
Ref | Expression |
---|---|
mt2d.1 | ⊢ (𝜑 → 𝜒) |
mt2d.2 | ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) |
Ref | Expression |
---|---|
mt2d | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt2d.1 | . 2 ⊢ (𝜑 → 𝜒) | |
2 | mt2d.2 | . . 3 ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) | |
3 | 2 | con2d 619 | . 2 ⊢ (𝜑 → (𝜒 → ¬ 𝜓)) |
4 | 1, 3 | mpd 13 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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 609 ax-in2 610 |
This theorem is referenced by: nsyl3 621 mt2i 639 en2lp 4536 recnz 9298 xnn0dcle 9752 fznuz 10051 uznfz 10052 pcadd 12286 oddennn 12340 |
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