Metamath Proof Explorer


Theorem nfnfc1

Description: The setvar x is bound in F/_ x A . (Contributed by Mario Carneiro, 11-Aug-2016)

Ref Expression
Assertion nfnfc1 𝑥 𝑥 𝐴

Proof

Step Hyp Ref Expression
1 df-nfc ( 𝑥 𝐴 ↔ ∀ 𝑦𝑥 𝑦𝐴 )
2 nfnf1 𝑥𝑥 𝑦𝐴
3 2 nfal 𝑥𝑦𝑥 𝑦𝐴
4 1 3 nfxfr 𝑥 𝑥 𝐴