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 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦

Proof

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