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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-pm2.18d | Structured version Visualization version GIF version |
Description: Deduction based on reductio ad absurdum. Copy of pm2.18d 127 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-pm2.18d.1 | ⊢ (𝜑 → (¬ 𝜓 → 𝜓)) |
Ref | Expression |
---|---|
wl-luk-pm2.18d | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-pm2.18d.1 | . 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜓)) | |
2 | ax-luk2 34703 | . 2 ⊢ ((¬ 𝜓 → 𝜓) → 𝜓) | |
3 | 1, 2 | wl-luk-syl 34707 | 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-luk1 34702 ax-luk2 34703 |
This theorem is referenced by: wl-luk-con4i 34710 wl-luk-mpi 34713 wl-luk-con1i 34721 wl-luk-ja 34722 |
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