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Theorem pm5.21ni 366
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 (𝜑𝜓)
pm5.21ni.2 (𝜒𝜓)
Assertion
Ref Expression
pm5.21ni 𝜓 → (𝜑𝜒))

Proof of Theorem pm5.21ni
StepHypRef Expression
1 pm5.21ni.1 . . 3 (𝜑𝜓)
21con3i 151 . 2 𝜓 → ¬ 𝜑)
3 pm5.21ni.2 . . 3 (𝜒𝜓)
43con3i 151 . 2 𝜓 → ¬ 𝜒)
52, 42falsed 365 1 𝜓 → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196
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 197
This theorem is referenced by:  pm5.21nii  367  norbi  873  pm5.54  1003  niabn  1006  csbprc  4124  ordsssuc2  5957  ndmovord  6971  ordsucelsuc  7169  brdomg  8119  suppeqfsuppbi  8445  funsnfsupp  8455  r1pw  8872  r1pwALT  8873  elixx3g  12393  elfz2  12540  bifald  34220  areaquad  38328
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