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Mirrors > Home > MPE Home > Th. List > merlem4 | Structured version Visualization version GIF version |
Description: Step 8 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
merlem4 | ⊢ (𝜏 → ((𝜏 → 𝜑) → (𝜃 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | meredith 1644 | . 2 ⊢ (((((𝜑 → 𝜑) → (¬ 𝜃 → ¬ 𝜃)) → 𝜃) → 𝜏) → ((𝜏 → 𝜑) → (𝜃 → 𝜑))) | |
2 | merlem3 1647 | . 2 ⊢ ((((((𝜑 → 𝜑) → (¬ 𝜃 → ¬ 𝜃)) → 𝜃) → 𝜏) → ((𝜏 → 𝜑) → (𝜃 → 𝜑))) → (𝜏 → ((𝜏 → 𝜑) → (𝜃 → 𝜑)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜏 → ((𝜏 → 𝜑) → (𝜃 → 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → 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: merlem5 1649 merlem6 1650 merlem7 1651 merlem12 1656 luk-2 1659 |
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