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Mirrors > Home > NFE Home > Th. List > mt3d | GIF version |
Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995.) |
Ref | Expression |
---|---|
mt3d.1 | ⊢ (φ → ¬ χ) |
mt3d.2 | ⊢ (φ → (¬ ψ → χ)) |
Ref | Expression |
---|---|
mt3d | ⊢ (φ → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt3d.1 | . 2 ⊢ (φ → ¬ χ) | |
2 | mt3d.2 | . . 3 ⊢ (φ → (¬ ψ → χ)) | |
3 | 2 | con1d 116 | . 2 ⊢ (φ → (¬ χ → ψ)) |
4 | 1, 3 | mpd 14 | 1 ⊢ (φ → ψ) |
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: mt3i 118 nsyl2 119 ecase23d 1285 nnsucelr 4428 enprmaplem5 6080 |
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