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Theorem hbnaev 2038
Description: Any variable is free in ¬ ∀𝑥𝑥 = 𝑦, if 𝑥 and 𝑦 are distinct. This condition is dropped in hbnae 2411, at the expense of more axiom dependencies. Instance of hbnaevg 2037. (Contributed by Wolf Lammen, 9-Apr-2021.)
Assertion
Ref Expression
hbnaev (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑦

Proof of Theorem hbnaev
StepHypRef Expression
1 hbnaevg 2037 1 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1520
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1762
This theorem is referenced by:  euae  2717
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