Theorem nfofr 6241

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 6235	. 2 |- oR R = { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
2		nfcv 2374	. . . 4 |- F/_ x ( dom u i^i dom v )
3		nfcv 2374	. . . . 5 |- F/_ x ( u ` w )
4		nfof.1	. . . . 5 |- F/_ x R
5		nfcv 2374	. . . . 5 |- F/_ x ( v ` w )
6	3, 4, 5	nfbr 4135	. . . 4 |- F/ x ( u ` w ) R ( v ` w )
7	2, 6	nfralxy 2570	. . 3 |- F/ x A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w )
8	7	nfopab 4157	. 2 |- F/_ x { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
9	1, 8	nfcxfr 2371	1 |- F/_ x oR R

Syntax hints:   F/_wnfc 2361   A.wral 2510   i^i cin 3199   class class class wbr 4088   {copab 4149   dom cdm 4725   ` cfv 5326   oRcofr 6233

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-ral 2515  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676  df-op 3678  df-br 4089  df-opab 4151  df-ofr 6235

This theorem is referenced by: (None)