Metamath Proof Explorer


Theorem nfrel

Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004) (Revised by Mario Carneiro, 15-Oct-2016)

Ref Expression
Hypothesis nfrel.1 ⊢ Ⅎ 𝑥 𝐴
Assertion nfrel Ⅎ 𝑥 Rel 𝐴

Proof

Step Hyp Ref Expression
1 nfrel.1 ⊢ Ⅎ 𝑥 𝐴
2 df-rel ⊢ ( Rel 𝐴 ↔ 𝐴 ⊆ ( V × V ) )
3 nfcv ⊢ Ⅎ 𝑥 ( V × V )
4 1 3 nfss ⊢ Ⅎ 𝑥 𝐴 ⊆ ( V × V )
5 2 4 nfxfr ⊢ Ⅎ 𝑥 Rel 𝐴