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Theorem trut 1641
Description: A proposition is equivalent to it being implied by . Closed form of trud 1642. Dual of dfnot 1651. It is to tbtru 1643 what a1bi 351 is to tbt 358. (Contributed by BJ, 26-Oct-2019.)
Assertion
Ref Expression
trut (𝜑 ↔ (⊤ → 𝜑))

Proof of Theorem trut
StepHypRef Expression
1 tru 1636 . 2
21a1bi 351 1 (𝜑 ↔ (⊤ → 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wtru 1633
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 197  df-tru 1635
This theorem is referenced by:  truimfal  1664
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