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Mirrors > Home > MPE Home > Th. List > merco1lem9 | Structured version Visualization version GIF version |
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1629. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
merco1lem9 | ⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | merco1lem8 1640 | . 2 ⊢ ((⊥ → 𝜑) → ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓))) | |
2 | merco1lem8 1640 | . 2 ⊢ (((⊥ → 𝜑) → ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓))) → ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1480 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-tru 1478 df-fal 1481 |
This theorem is referenced by: merco1lem12 1644 merco1lem14 1646 merco1lem17 1649 merco1lem18 1650 retbwax1 1651 |
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