Theorem hbnae-o

Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in Megill p. 446 (p. 14 of the preprint). Version of hbnae using ax-c11 . (Contributed by NM, 13-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	hbnae-o	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦 )

Proof

Step	Hyp	Ref	Expression
1		hbae-o	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ∀ 𝑥 𝑥 = 𝑦 )
2	1	hbn	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦 )