Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfxor5 Structured version   Visualization version   Unicode version
Theorem dfxor5 38059
Description: Express exclusive-or in terms of implication and negation. Statement in [Frege1879] p. 12. (Contributed by RP, 14-Apr-2020.)
Assertion
Ref Expression
dfxor5 |- ( ( ph \/_ ps ) <-> -. ( ( ph -> -. ps ) -> -. ( -. ph -> ps ) ) )
Proof of Theorem dfxor5
StepHypRef Expression
1 dfxor4 38058 . 2 |- ( ( ph \/_ ps ) <-> -. ( ( -. ph -> ps ) -> -. ( ph -> -. ps ) ) )
2 con2b 349 . 2 |- ( ( ( -. ph -> ps ) -> -. ( ph -> -. ps ) ) <-> ( ( ph -> -. ps ) -> -. ( -. ph -> ps ) ) )
31, 2xchbinx 324 1 |- ( ( ph \/_ ps ) <-> -. ( ( ph -> -. ps ) -> -. ( -. ph -> ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/_ wxo 1464
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 197  df-or 385  df-an 386  df-xor 1465
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator