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Theorem nfofr 5995
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 5990 . 2  |-  oR R  =  { <. u ,  v >.  |  A. w  e.  ( dom  u  i^i  dom  v )
( u `  w
) R ( v `
 w ) }
2 nfcv 2282 . . . 4  |-  F/_ x
( dom  u  i^i  dom  v )
3 nfcv 2282 . . . . 5  |-  F/_ x
( u `  w
)
4 nfof.1 . . . . 5  |-  F/_ x R
5 nfcv 2282 . . . . 5  |-  F/_ x
( v `  w
)
63, 4, 5nfbr 3981 . . . 4  |-  F/ x
( u `  w
) R ( v `
 w )
72, 6nfralxy 2474 . . 3  |-  F/ x A. w  e.  ( dom  u  i^i  dom  v
) ( u `  w ) R ( v `  w )
87nfopab 4003 . 2  |-  F/_ x { <. u ,  v
>.  |  A. w  e.  ( dom  u  i^i 
dom  v ) ( u `  w ) R ( v `  w ) }
91, 8nfcxfr 2279 1  |-  F/_ x  oR R
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2269   A.wral 2417    i^i cin 3074   class class class wbr 3936   {copab 3995   dom cdm 4546   ` cfv 5130    oRcofr 5988
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-br 3937  df-opab 3997  df-ofr 5990
This theorem is referenced by: (None)
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