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Theorem 2false 340
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Hypotheses
Ref Expression
2false.1  |-  -.  ph
2false.2  |-  -.  ps
Assertion
Ref Expression
2false  |-  ( ph  <->  ps )

Proof of Theorem 2false
StepHypRef Expression
1 2false.1 . . 3  |-  -.  ph
2 2false.2 . . 3  |-  -.  ps
31, 22th 231 . 2  |-  ( -. 
ph 
<->  -.  ps )
43con4bii 289 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177
This theorem is referenced by:  bianfi  892  bifal  1336  iun0  4147  0iun  4148  xp0r  4956  cnv0  5275  co02  5383  0er  6940  00lss  16018  00ply1bas  16634  dandysum2p2e4  27919  pexmidlem8N  30774
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 178
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