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Theorem pm5.21im 686
Description: Two propositions are equivalent if they are both false. Closed form of 2false 691. Equivalent to a biimpr 129-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.21im  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )

Proof of Theorem pm5.21im
StepHypRef Expression
1 pm5.21 685 . 2  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
21ex 114 1  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nbn2  687
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