Theorem nfrel 5719

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 5621	. 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V))
2		nfrel.1	. . 3 ⊢ Ⅎ𝑥𝐴
3		nfcv 2894	. . 3 ⊢ Ⅎ𝑥(V × V)
4	2, 3	nfss 3922	. 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V)
5	1, 4	nfxfr 1854	1 ⊢ Ⅎ𝑥Rel 𝐴

Syntax hints:  Ⅎwnf 1784  Ⅎwnfc 2879  Vcvv 3436   ⊆ wss 3897   × cxp 5612  Rel wrel 5619

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-10 2144  ax-11 2160  ax-12 2180

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1781  df-nf 1785  df-clel 2806  df-nfc 2881  df-ral 3048  df-ss 3914  df-rel 5621

This theorem is referenced by:  nffun  6504