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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-ax2 | Structured version Visualization version GIF version |
Description: ax-2 7 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-ax2 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-pm2.21 36782 | . . 3 ⊢ (¬ 𝜑 → (𝜑 → 𝜒)) | |
2 | 1 | wl-luk-a1d 36786 | . 2 ⊢ (¬ 𝜑 → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) |
3 | wl-luk-imim2 36785 | . 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) | |
4 | 2, 3 | wl-luk-ja 36784 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 36764 ax-luk2 36765 ax-luk3 36766 |
This theorem is referenced by: wl-luk-pm2.04 36790 |
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