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Theorem pm5.21ni 382
 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 157 . 2 𝜓 → ¬ 𝜑)
3 pm5.21ni.2 . . 3 (𝜒𝜓)
43con3i 157 . 2 𝜓 → ¬ 𝜒)
52, 42falsed 380 1 𝜓 → (𝜑𝜒))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 209 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 210 This theorem is referenced by:  pm5.21nii  383  norbi  884  pm5.54  1015  niabn  1018  csbprc  4316  ordsssuc2  6251  ndmovord  7322  ordsucelsuc  7521  brdomg  8506  suppeqfsuppbi  8835  funsnfsupp  8845  r1pw  9262  r1pwALT  9263  elixx3g  12743  elfz2  12896  bifald  35524  areaquad  40159
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