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Theorem pm5.21ni 342
Description: Two propositions implying a false one are equivalent. (Contributed by NM, 16-Feb-1996.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Hypotheses
Ref Expression
pm5.21ni.1  |-  ( ph  ->  ps )
pm5.21ni.2  |-  ( ch 
->  ps )
Assertion
Ref Expression
pm5.21ni  |-  ( -. 
ps  ->  ( ph  <->  ch )
)

Proof of Theorem pm5.21ni
StepHypRef Expression
1 pm5.21ni.1 . . 3  |-  ( ph  ->  ps )
21con3i 129 . 2  |-  ( -. 
ps  ->  -.  ph )
3 pm5.21ni.2 . . 3  |-  ( ch 
->  ps )
43con3i 129 . 2  |-  ( -. 
ps  ->  -.  ch )
52, 42falsed 341 1  |-  ( -. 
ps  ->  ( ph  <->  ch )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177
This theorem is referenced by:  pm5.21nii  343  pm5.54  871  niabn  918  ordsssuc2  4670  ordsucelsuc  4802  ndmovord  6237  brdomg  7118  r1pw  7771  r1pwOLD  7772  elixx3g  10929  elfz2  11050  wl-pm5.32  26229
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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