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Mirrors > Home > MPE Home > Th. List > monothetic | Structured version Visualization version GIF version |
Description: Two self-implications (see id 22) are equivalent. This theorem, rather trivial in our axiomatization, is (the biconditional form of) a standard axiom for monothetic BCI logic. This is the most general theorem of which trujust 1603 is an instance. Relatedly, this would be the justification theorem if the definition of ⊤ were dftru2 1607. (Contributed by BJ, 7-Sep-2022.) |
Ref | Expression |
---|---|
monothetic | ⊢ ((𝜑 → 𝜑) ↔ (𝜓 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝜑 → 𝜑) | |
2 | id 22 | . 2 ⊢ (𝜓 → 𝜓) | |
3 | 1, 2 | 2th 256 | 1 ⊢ ((𝜑 → 𝜑) ↔ (𝜓 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 |
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 199 |
This theorem is referenced by: trujust 1603 |
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