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Theorem tbt 240
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 239 . . 3 ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))
32pm5.74ri 174 . 2 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
41, 3ax-mp 7 1 (𝜓 ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  tbtru  1269  exists1  2012  reu6  2753  eqv  3268  vprc  3916  bj-vprc  10403
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