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Theorem tbt 246
Description: A wff is equivalent to its equivalence with truth. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypothesis
Ref Expression
tbt.1 𝜑
Assertion
Ref Expression
tbt (𝜓 ↔ (𝜓𝜑))

Proof of Theorem tbt
StepHypRef Expression
1 tbt.1 . 2 𝜑
2 ibibr 245 . . 3 ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))
32pm5.74ri 180 . 2 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
41, 3ax-mp 5 1 (𝜓 ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  tbtru  1326  exists1  2073  reu6  2846  eqv  3352  vnex  4029  bj-vprc  13021
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