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Theorem tbt 236
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 235 . . 3 ((φψ) ↔ (φ → (ψφ)))
32pm5.74ri 170 . 2 (φ → (ψ ↔ (ψφ)))
41, 3ax-mp 7 1 (ψ ↔ (ψφ))
Colors of variables: wff set class
Syntax hints:  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  tbtru  1238  exists1  1978  reu6  2707  eqv  3217  vprc  3862  bj-vprc  7119
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