Theorem wl-naevhba1v 37499

Description: An instance of hbn1w 2046 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.

Step	Hyp	Ref	Expression
1		equequ1 2024	. 2 ⊢ (𝑥 = 𝑧 → (𝑥 = 𝑦 ↔ 𝑧 = 𝑦))
2	1	hbn1w 2046	1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑥 ¬ ∀𝑥 𝑥 = 𝑦)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780

This theorem is referenced by: (None)