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Mirrors > Home > MPE Home > Th. List > pm2.01d | Structured version Visualization version GIF version |
Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 5-Mar-2013.) |
Ref | Expression |
---|---|
pm2.01d.1 | ⊢ (𝜑 → (𝜓 → ¬ 𝜓)) |
Ref | Expression |
---|---|
pm2.01d | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.01d.1 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓)) | |
2 | id 22 | . 2 ⊢ (¬ 𝜓 → ¬ 𝜓) | |
3 | 1, 2 | pm2.61d1 180 | 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: pm2.65d 195 pm2.01da 798 swopo 5600 onssneli 6481 oalimcl 8560 rankcf 10772 prlem934 11028 supsrlem 11106 rpnnen1lem5 12965 rennim 15186 smu01lem 16426 opsrtoslem2 21617 cfinufil 23432 alexsub 23549 ostth3 27141 4cyclusnfrgr 29545 cvnref 31544 pconnconn 34222 untelirr 34677 dfon2lem4 34758 heiborlem10 36688 lindslinindsimp1 47138 |
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