MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfbi1 Unicode version

Theorem dfbi1 192
Description: Relate the biconditional connective to primitive connectives. See dfbi1ALT 193 for an unusual version proved directly from axioms. (Contributed by NM, 29-Dec-1992.)
Assertion
Ref Expression
dfbi1

Proof of Theorem dfbi1
StepHypRef Expression
1 df-bi 185 . . 3
2 simplim 151 . . 3
31, 2ax-mp 5 . 2
4 bi3 187 . . 3
54impi 148 . 2
63, 5impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184
This theorem is referenced by:  bi2  198  dfbi2  628  tbw-bijust  1531  rb-bijust  1582  axrepprim  29074  axacprim  29079
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 185
  Copyright terms: Public domain W3C validator