Theorem nfrel 4858

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 4779	. 2 |- ( Rel A <-> A C_ ( _V X. _V ) )
2		nfrel.1	. . 3 |- F/_ x A
3		nfcv 2392	. . 3 |- F/_ x ( _V X. _V )
4	2, 3	nfss 3241	. 2 |- F/ x A C_ ( _V X. _V )
5	1, 4	nfxfr 1527	1 |- F/ x Rel A

Syntax hints:   F/wnf 1513   F/_wnfc 2379   _Vcvv 2821   C_ wss 3220   X. cxp 4770   Rel wrel 4777

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-in 3226  df-ss 3233  df-rel 4779

This theorem is referenced by:  nffun  5398