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Theorem biimt 325
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 6 . 2 (ψ → (φψ))
2 pm2.27 35 . 2 (φ → ((φψ) → ψ))
31, 2impbid2 195 1 (φ → (ψ ↔ (φψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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 177
This theorem is referenced by:  pm5.5  326  a1bi  327  mtt  329  abai  770  dedlem0a  918  ceqsralt  2882  reu8  3032  csbiebt  3172  r19.3rz  3641  r19.3rzv  3643  ralidm  3653  fncnv  5158
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