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

Theorem sbbid 1723
Description: Deduction substituting both sides of a biconditional. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
sbbid.1
sbbid.2
Assertion
Ref Expression
sbbid

Proof of Theorem sbbid
StepHypRef Expression
1 sbbid.1 . . 3
2 sbbid.2 . . 3
31, 2alrimih 1355 . 2
4 spsbbi 1722 . 2
53, 4syl 14 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240  wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbcomxyyz  1843
  Copyright terms: Public domain W3C validator