MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  xnor Structured version   Visualization version   GIF version

Theorem xnor 1636
Description: Two ways to write XNOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xnor ((𝜑𝜓) ↔ ¬ (𝜑𝜓))

Proof of Theorem xnor
StepHypRef Expression
1 df-xor 1635 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 349 1 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wxo 1634
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 199  df-xor 1635
This theorem is referenced by:  xorass  1638  xorneg2  1644  hadbi  1708  had0  1714  tsxo1  34430  tsxo2  34431
  Copyright terms: Public domain W3C validator