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Theorem monothetic 258
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 ((𝜑𝜑) ↔ (𝜓𝜓))

Proof of Theorem monothetic
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
2 id 22 . 2 (𝜓𝜓)
31, 22th 256 1 ((𝜑𝜑) ↔ (𝜓𝜓))
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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