![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > pm2.01d | GIF version |
Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Revised by Mario Carneiro, 31-Jan-2015.) |
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 | pm2.01 616 | . 2 ⊢ ((𝜓 → ¬ 𝜓) → ¬ 𝜓) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in1 614 |
This theorem is referenced by: pm2.01da 636 pm2.65d 660 pm5.19 706 mtord 783 swopo 4302 rennim 10982 absle 11069 bj-nnclavius 14111 |
Copyright terms: Public domain | W3C validator |