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Theorem biimt 234
Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996.)
Assertion
Ref Expression
biimt (𝜑 → (𝜓 ↔ (𝜑𝜓)))

Proof of Theorem biimt
StepHypRef Expression
1 ax-1 5 . 2 (𝜓 → (𝜑𝜓))
2 pm2.27 39 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
31, 2impbid2 135 1 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  pm5.5  235  a1bi  236  abai  502  dedlem0a  886  ceqsralt  2598  reu8  2760  csbiebt  2914  r19.3rm  3338  fncnv  4993  ovmpt2dxf  5654  brecop  6227
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