ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3bitr3d Structured version   Unicode version

Theorem 3bitr3d 207
Description: Deduction from transitivity of biconditional. Useful for converting conditional definitions in a formula. (Contributed by NM, 24-Apr-1996.)
Hypotheses
Ref Expression
3bitr3d.1
3bitr3d.2
3bitr3d.3
Assertion
Ref Expression
3bitr3d

Proof of Theorem 3bitr3d
StepHypRef Expression
1 3bitr3d.2 . . 3
2 3bitr3d.1 . . 3
31, 2bitr3d 179 . 2
4 3bitr3d.3 . 2
53, 4bitrd 177 1
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:  csbcomg  2867  eloprabga  5533  ereldm  6085  subcan  7062  conjmulap  7487  ltrec  7630  divelunit  8640  fseq1m1p1  8727  fzm1  8732
  Copyright terms: Public domain W3C validator