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Mirrors > Home > MPE Home > Th. List > mt4d | Structured version Visualization version GIF version |
Description: Modus tollens deduction. Deduction form of mt4 115. (Contributed by NM, 9-Jun-2006.) |
Ref | Expression |
---|---|
mt4d.1 | ⊢ (𝜑 → 𝜓) |
mt4d.2 | ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
Ref | Expression |
---|---|
mt4d | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt4d.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | mt4d.2 | . . 3 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) | |
3 | 2 | con4d 114 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
4 | 1, 3 | mpd 15 | 1 ⊢ (𝜑 → 𝜒) |
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: mt4i 153 fin1a2s 9236 gchinf 9479 pwfseqlem4 9484 pcfac 15603 prmreclem3 15622 sylow1lem1 18013 irredrmul 18707 mdetunilem9 20426 ioorcl2 23340 itg2gt0 23527 mdegmullem 23838 atom1d 29212 notnotrALT 38735 fourierdlem79 40402 |
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