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Mirrors > Home > MPE Home > Th. List > luklem8 | Structured version Visualization version GIF version |
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
luklem8 | ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | luk-1 1571 | . 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓))) | |
2 | luklem7 1580 | . 2 ⊢ (((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓))) → ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → 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: ax2 1583 |
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