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Theorem pm5.21ni 606
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 549 . 2 ψ → ¬ φ)
3 pm5.21ni.2 . . 3 (χψ)
43con3i 549 . 2 ψ → ¬ χ)
52, 42falsed 605 1 ψ → (φχ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  niabn  862
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