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Theorem xnor 1406
Description: Two ways to write XNOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xnor  |-  ( (
ph 
<->  ps )  <->  -.  ( ph  \/_  ps ) )

Proof of Theorem xnor
StepHypRef Expression
1 df-xor 1405 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
21con2bii 334 1  |-  ( (
ph 
<->  ps )  <->  -.  ( ph  \/_  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 188    \/_ wxo 1404
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 189  df-xor 1405
This theorem is referenced by:  xorass  1408  xorneg2  1415  xorneg1OLD  1417  hadbi  1500  had0  1506  elsymdifxor  3668  tsxo1  32372  tsxo2  32373
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