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Theorem bj-denot 31849
Description: A weakening of ax-6 1875 and ax6v 1876. (Contributed by BJ, 4-Apr-2021.) (New usage is discouraged.)
Assertion
Ref Expression
bj-denot (𝑥 = 𝑥 → ¬ ∀𝑦 ¬ 𝑦 = 𝑥)
Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-denot
StepHypRef Expression
1 ax6v 1876 . 2 ¬ ∀𝑦 ¬ 𝑦 = 𝑥
21a1i 11 1 (𝑥 = 𝑥 → ¬ ∀𝑦 ¬ 𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-6 1875
This theorem is referenced by: (None)
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