Theorem nfrel 4761

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 4683	. 2 |- ( Rel A <-> A C_ ( _V X. _V ) )
2		nfrel.1	. . 3 |- F/_ x A
3		nfcv 2348	. . 3 |- F/_ x ( _V X. _V )
4	2, 3	nfss 3186	. 2 |- F/ x A C_ ( _V X. _V )
5	1, 4	nfxfr 1497	1 |- F/ x Rel A

Syntax hints:   F/wnf 1483   F/_wnfc 2335   _Vcvv 2772   C_ wss 3166   X. cxp 4674   Rel wrel 4681

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-ral 2489  df-in 3172  df-ss 3179  df-rel 4683

This theorem is referenced by:  nffun  5295