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Theorem pm5.21im 338
Description: Two propositions are equivalent if they are both false. Closed form of 2false 339. Equivalent to a bi2 189-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.)
Assertion
Ref Expression
pm5.21im  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )

Proof of Theorem pm5.21im
StepHypRef Expression
1 nbn2 334 . 2  |-  ( -. 
ph  ->  ( -.  ps  <->  (
ph 
<->  ps ) ) )
21biimpd 198 1  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  pm5.21ndd  343  pm5.21  831
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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