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Theorem nfofr 5797
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.
StepHypRef Expression
1 df-ofr 5792 . 2  |-  oR R  =  { <. u ,  v >.  |  A. w  e.  ( dom  u  i^i  dom  v )
( u `  w
) R ( v `
 w ) }
2 nfcv 2223 . . . 4  |-  F/_ x
( dom  u  i^i  dom  v )
3 nfcv 2223 . . . . 5  |-  F/_ x
( u `  w
)
4 nfof.1 . . . . 5  |-  F/_ x R
5 nfcv 2223 . . . . 5  |-  F/_ x
( v `  w
)
63, 4, 5nfbr 3855 . . . 4  |-  F/ x
( u `  w
) R ( v `
 w )
72, 6nfralxy 2408 . . 3  |-  F/ x A. w  e.  ( dom  u  i^i  dom  v
) ( u `  w ) R ( v `  w )
87nfopab 3872 . 2  |-  F/_ x { <. u ,  v
>.  |  A. w  e.  ( dom  u  i^i 
dom  v ) ( u `  w ) R ( v `  w ) }
91, 8nfcxfr 2220 1  |-  F/_ x  oR R
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2210   A.wral 2353    i^i cin 2983   class class class wbr 3811   {copab 3864   dom cdm 4401   ` cfv 4969    oRcofr 5790
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-v 2614  df-un 2988  df-sn 3428  df-pr 3429  df-op 3431  df-br 3812  df-opab 3866  df-ofr 5792
This theorem is referenced by: (None)
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