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Theorem notbinot1 31758
Description: Simplification rule of negation across a biimplication. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
notbinot1  |-  ( -.  ( -.  ph  <->  ps )  <->  (
ph 
<->  ps ) )

Proof of Theorem notbinot1
StepHypRef Expression
1 nbbn 356 . . 3  |-  ( ( -.  ph  <->  ps )  <->  -.  ( ph 
<->  ps ) )
21bicomi 202 . 2  |-  ( -.  ( ph  <->  ps )  <->  ( -.  ph  <->  ps ) )
32con1bii 329 1  |-  ( -.  ( -.  ph  <->  ps )  <->  (
ph 
<->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184
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
This theorem is referenced by:  bicontr  31759
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