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Metamath Proof Explorer

Theorem nfnae

Description: All variables are effectively bound in a distinct variable specifier. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfnaew when possible. (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

		Ref	Expression
	Assertion	nfnae	⊢ Ⅎ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦

Proof

Step	Hyp	Ref	Expression
1		nfae	⊢ Ⅎ 𝑧 ∀ 𝑥 𝑥 = 𝑦
2	1	nfn	⊢ Ⅎ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦