Theorem nfrel 4744

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 4666	. 2 |- ( Rel A <-> A C_ ( _V X. _V ) )
2		nfrel.1	. . 3 |- F/_ x A
3		nfcv 2336	. . 3 |- F/_ x ( _V X. _V )
4	2, 3	nfss 3172	. 2 |- F/ x A C_ ( _V X. _V )
5	1, 4	nfxfr 1485	1 |- F/ x Rel A

Syntax hints:   F/wnf 1471   F/_wnfc 2323   _Vcvv 2760   C_ wss 3153   X. cxp 4657   Rel wrel 4664

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-in 3159  df-ss 3166  df-rel 4666

This theorem is referenced by:  nffun  5277