Metamath Proof Explorer


Theorem nfae

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

Ref Expression
Assertion nfae 𝑧𝑥 𝑥 = 𝑦

Proof

Step Hyp Ref Expression
1 hbae ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧𝑥 𝑥 = 𝑦 )
2 1 nf5i 𝑧𝑥 𝑥 = 𝑦