ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  biimt Structured version   GIF version

Theorem biimt 230
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 35 . 2 (φ → ((φψ) → ψ))
31, 2impbid2 131 1 (φ → (ψ ↔ (φψ)))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  pm5.5  231  a1bi  232  abai  482  dedlem0a  863  ceqsralt  2558  reu8  2714  csbiebt  2863  r19.3rmOLD  3287  r19.3rm  3289  fncnv  4891  ovmpt2dxf  5549  brecop  6107
  Copyright terms: Public domain W3C validator