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Theorem nexr 2192
Description: Inference associated with the contrapositive of 19.8a 2181. (Contributed by Jeff Hankins, 26-Jul-2009.)
Hypothesis
Ref Expression
nexr.1 ¬ ∃𝑥𝜑
Assertion
Ref Expression
nexr ¬ 𝜑

Proof of Theorem nexr
StepHypRef Expression
1 nexr.1 . 2 ¬ ∃𝑥𝜑
2 19.8a 2181 . 2 (𝜑 → ∃𝑥𝜑)
31, 2mto 200 1 ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2178
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  alimp-surprise  45247
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