MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bijust Structured version   Visualization version   Unicode version
Theorem bijust 195
Description: Theorem used to justify definition of biconditional df-bi 197. (Contributed by NM, 11-May-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Assertion
Ref Expression
bijust |- -. ( ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) -> -. ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) )
Proof of Theorem bijust
StepHypRef Expression
1 id 22 . 2 |- ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) )
2 pm2.01 180 . 2 |- ( ( ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) -> -. ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) ) -> -. ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) )
31, 2mt2 191 1 |- -. ( ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) -> -. ( -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) -> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator