Theorem nfrel 4689

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 4611	. 2 |- ( Rel A <-> A C_ ( _V X. _V ) )
2		nfrel.1	. . 3 |- F/_ x A
3		nfcv 2308	. . 3 |- F/_ x ( _V X. _V )
4	2, 3	nfss 3135	. 2 |- F/ x A C_ ( _V X. _V )
5	1, 4	nfxfr 1462	1 |- F/ x Rel A

Syntax hints:   F/wnf 1448   F/_wnfc 2295   _Vcvv 2726   C_ wss 3116   X. cxp 4602   Rel wrel 4609

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-ral 2449  df-in 3122  df-ss 3129  df-rel 4611

This theorem is referenced by:  nffun  5211