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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 150 . 2 𝜓 → ¬ 𝜑)
3 pm5.21ni.2 . . 3 (𝜒𝜓)
43con3i 150 . 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  940  pm5.54  981  niabn  1002  csbprc  4123  ordsssuc2  5975  ndmovord  6989  ordsucelsuc  7187  brdomg  8131  suppeqfsuppbi  8454  funsnfsupp  8464  r1pw  8881  r1pwALT  8882  elixx3g  12381  elfz2  12526  bifald  34201  areaquad  38304
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