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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 9250 phpeqdOLD 9260 fin1a2s 10452 gchinf 10695 pwfseqlem4 10700 pcfac 16933 prmreclem3 16952 sylow1lem1 19631 irredrmul 20444 mdetunilem9 22642 ioorcl2 25621 itg2gt0 25810 mdegmullem 26132 atom1d 32382 rr-phpd 44199 notnotrALT 44527 fourierdlem79 46141 |
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