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Theorem pm5.21ni 377
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 154 . 2 𝜓 → ¬ 𝜑)
3 pm5.21ni.2 . . 3 (𝜒𝜓)
43con3i 154 . 2 𝜓 → ¬ 𝜒)
52, 42falsed 376 1 𝜓 → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 206
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 207
This theorem is referenced by:  pm5.21nii  378  norbi  886  pm5.54  1019  niabn  1022  sbccomlem  3868  ab0w  4378  csbprc  4408  ralf0  4513  ordsssuc2  6474  ndmovord  7624  ordsucelsuc  7843  brdomg  8998  brdomgOLD  8999  suppeqfsuppbi  9420  funsnfsupp  9433  r1pw  9886  r1pwALT  9887  elixx3g  13401  elfz2  13555  bifald  38095  areaquad  43233
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