Theorem nfofr 6251

Description: Hypothesis builder for function relation. (Contributed by Mario Carneiro, 28-Jul-2014.)

Hypothesis

Ref	Expression
nfof.1	|- F/_ x R

Assertion

Ref	Expression
nfofr	|- F/_ x oR R

Proof of Theorem nfofr

Dummy variables u v w are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-ofr 6245	. 2 |- oR R = { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
2		nfcv 2375	. . . 4 |- F/_ x ( dom u i^i dom v )
3		nfcv 2375	. . . . 5 |- F/_ x ( u ` w )
4		nfof.1	. . . . 5 |- F/_ x R
5		nfcv 2375	. . . . 5 |- F/_ x ( v ` w )
6	3, 4, 5	nfbr 4140	. . . 4 |- F/ x ( u ` w ) R ( v ` w )
7	2, 6	nfralxy 2571	. . 3 |- F/ x A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w )
8	7	nfopab 4162	. 2 |- F/_ x { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
9	1, 8	nfcxfr 2372	1 |- F/_ x oR R

Syntax hints:   F/_wnfc 2362   A.wral 2511   i^i cin 3200   class class class wbr 4093   {copab 4154   dom cdm 4731   ` cfv 5333   oRcofr 6243

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-ral 2516  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-op 3682  df-br 4094  df-opab 4156  df-ofr 6245

This theorem is referenced by: (None)