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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 116. (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 115 | . 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 118 pm2.18d 127 phpeqd 8700 fin1a2s 9830 gchinf 10073 pwfseqlem4 10078 pcfac 16229 prmreclem3 16248 sylow1lem1 18717 irredrmul 19451 mdetunilem9 21223 ioorcl2 24167 itg2gt0 24355 mdegmullem 24666 atom1d 30124 rr-phpd 40555 notnotrALT 40856 fourierdlem79 42464 |
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