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Theorem wl-naevhba1v 33635
Description: An instance of hbn1w 2124 applied to equality. (Contributed by Wolf Lammen, 7-Apr-2021.)
Assertion
Ref Expression
wl-naevhba1v (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑥 ¬ ∀𝑥 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑦

Proof of Theorem wl-naevhba1v
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 equequ1 2107 . 2 (𝑥 = 𝑧 → (𝑥 = 𝑦𝑧 = 𝑦))
21hbn1w 2124 1 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑥 ¬ ∀𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854
This theorem is referenced by: (None)
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