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Theorem pm5.21im 350
Description: Two propositions are equivalent if they are both false. Closed form of 2false 351. Equivalent to a biimpr 201-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 346 . 2  |-  ( -. 
ph  ->  ( -.  ps  <->  (
ph 
<->  ps ) ) )
21biimpd 210 1  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187
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 188
This theorem is referenced by:  pm5.21ndd  355  pm5.21  866
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