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Mirrors > Home > MPE Home > Th. List > bijust | Structured version Visualization version GIF version |
Description: Theorem used to justify the definition of the biconditional df-bi 206. Instance of bijust0 203. (Contributed by NM, 11-May-1999.) |
Ref | Expression |
---|---|
bijust | ⊢ ¬ ((¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑)) → ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑))) → ¬ (¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑)) → ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bijust0 203 | 1 ⊢ ¬ ((¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑)) → ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑))) → ¬ (¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑)) → ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 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: (None) |
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