Theorem nfrel 5742

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 5645	. 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V))
2		nfrel.1	. . 3 ⊢ Ⅎ𝑥𝐴
3		nfcv 2891	. . 3 ⊢ Ⅎ𝑥(V × V)
4	2, 3	nfss 3939	. 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V)
5	1, 4	nfxfr 1853	1 ⊢ Ⅎ𝑥Rel 𝐴

Syntax hints:  Ⅎwnf 1783  Ⅎwnfc 2876  Vcvv 3447   ⊆ wss 3914   × cxp 5636  Rel wrel 5643

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-10 2142  ax-11 2158  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1780  df-nf 1784  df-clel 2803  df-nfc 2878  df-ral 3045  df-ss 3931  df-rel 5645

This theorem is referenced by:  nffun  6539