Theorem nfrel 4804

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	|- F/_ x A

Assertion

Ref	Expression
nfrel	|- F/ x Rel A

Proof of Theorem nfrel

Step	Hyp	Ref	Expression
1		df-rel 4726	. 2 |- ( Rel A <-> A C_ ( _V X. _V ) )
2		nfrel.1	. . 3 |- F/_ x A
3		nfcv 2372	. . 3 |- F/_ x ( _V X. _V )
4	2, 3	nfss 3217	. 2 |- F/ x A C_ ( _V X. _V )
5	1, 4	nfxfr 1520	1 |- F/ x Rel A

Syntax hints:   F/wnf 1506   F/_wnfc 2359   _Vcvv 2799   C_ wss 3197   X. cxp 4717   Rel wrel 4724

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-in 3203  df-ss 3210  df-rel 4726

This theorem is referenced by:  nffun  5341