Theorem nfofr 6299

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 6293	. 2 |- oR R = { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
2		nfcv 2392	. . . 4 |- F/_ x ( dom u i^i dom v )
3		nfcv 2392	. . . . 5 |- F/_ x ( u ` w )
4		nfof.1	. . . . 5 |- F/_ x R
5		nfcv 2392	. . . . 5 |- F/_ x ( v ` w )
6	3, 4, 5	nfbr 4172	. . . 4 |- F/ x ( u ` w ) R ( v ` w )
7	2, 6	nfralxy 2588	. . 3 |- F/ x A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w )
8	7	nfopab 4194	. 2 |- F/_ x { <. u , v >. | A. w e. ( dom u i^i dom v ) ( u ` w ) R ( v ` w ) }
9	1, 8	nfcxfr 2389	1 |- F/_ x oR R

Syntax hints:   F/_wnfc 2379   A.wral 2528   i^i cin 3219   class class class wbr 4125   {copab 4186   dom cdm 4769   ` cfv 5372   oRcofr 6291

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-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-v 2823  df-un 3224  df-sn 3711  df-pr 3712  df-op 3714  df-br 4126  df-opab 4188  df-ofr 6293

This theorem is referenced by: (None)