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Mirrors > Home > MPE Home > Th. List > mt3 | Structured version Visualization version GIF version |
Description: A rule similar to modus tollens. Inference associated with con1i 149. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.) |
Ref | Expression |
---|---|
mt3.1 | ⊢ ¬ 𝜓 |
mt3.2 | ⊢ (¬ 𝜑 → 𝜓) |
Ref | Expression |
---|---|
mt3 | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt3.1 | . . 3 ⊢ ¬ 𝜓 | |
2 | mt3.2 | . . 3 ⊢ (¬ 𝜑 → 𝜓) | |
3 | 1, 2 | mto 200 | . 2 ⊢ ¬ ¬ 𝜑 |
4 | 3 | notnotri 133 | 1 ⊢ 𝜑 |
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: dfbi1 216 wfrlem16 8079 sinhalfpilem 25366 equidq 36688 etransc 43514 |
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