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Theorem pm5.21ni 341
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 127 . 2 ψ → ¬ φ)
3 pm5.21ni.2 . . 3 (χψ)
43con3i 127 . 2 ψ → ¬ χ)
52, 42falsed 340 1 ψ → (φχ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176
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 177
This theorem is referenced by:  pm5.21nii  342  pm5.54  870  niabn  917  ndmovord  5620
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