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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-pm2.27 | Structured version Visualization version GIF version |
Description: This theorem, called "Assertion", can be thought of as closed form of modus ponens ax-mp 5. Theorem *2.27 of [WhiteheadRussell] p. 104. Copy of pm2.27 42 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-pm2.27 | ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-ax1 35605 | . . 3 ⊢ (𝜑 → (¬ 𝜓 → 𝜑)) | |
2 | ax-luk1 35590 | . . 3 ⊢ ((¬ 𝜓 → 𝜑) → ((𝜑 → 𝜓) → (¬ 𝜓 → 𝜓))) | |
3 | 1, 2 | wl-luk-syl 35595 | . 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → (¬ 𝜓 → 𝜓))) |
4 | ax-luk2 35591 | . 2 ⊢ ((¬ 𝜓 → 𝜓) → 𝜓) | |
5 | 3, 4 | wl-luk-imtrdi 35603 | 1 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35590 ax-luk2 35591 ax-luk3 35592 |
This theorem is referenced by: wl-luk-com12 35607 |
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