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Theorem nexdvOLD 1863
 Description: Obsolete proof of nexdv 1862 as of 10-Oct-2021. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 13-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nexdv.1 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
nexdvOLD (𝜑 → ¬ ∃𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nexdvOLD
StepHypRef Expression
1 nexdv.1 . . 3 (𝜑 → ¬ 𝜓)
21alrimiv 1853 . 2 (𝜑 → ∀𝑥 ¬ 𝜓)
3 alnex 1704 . 2 (∀𝑥 ¬ 𝜓 ↔ ¬ ∃𝑥𝜓)
42, 3sylib 208 1 (𝜑 → ¬ ∃𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1479  ∃wex 1702 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837 This theorem depends on definitions:  df-bi 197  df-ex 1703 This theorem is referenced by: (None)
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