Theorem nfrel 5750

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

Hypothesis

Ref	Expression
nfrel.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfrel	⊢ Ⅎ𝑥Rel 𝐴

Proof of Theorem nfrel

Step	Hyp	Ref	Expression
1		df-rel 5652	. 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V))
2		nfrel.1	. . 3 ⊢ Ⅎ𝑥𝐴
3		nfcv 2923	. . 3 ⊢ Ⅎ𝑥(V × V)
4	2, 3	nfss 3929	. 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V)
5	1, 4	nfxfr 1872	1 ⊢ Ⅎ𝑥Rel 𝐴

Syntax hints:  Ⅎwnf 1802  Ⅎwnfc 2908  Vcvv 3453   ⊆ wss 3904   × cxp 5643  Rel wrel 5650

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-10 2174  ax-11 2190  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-ex 1799  df-nf 1803  df-clel 2836  df-nfc 2910  df-ral 3076  df-ss 3921  df-rel 5652

This theorem is referenced by:  nffun  6538