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Theorem nfofr 5900
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 5895 . 2  |-  oR R  =  { <. u ,  v >.  |  A. w  e.  ( dom  u  i^i  dom  v )
( u `  w
) R ( v `
 w ) }
2 nfcv 2235 . . . 4  |-  F/_ x
( dom  u  i^i  dom  v )
3 nfcv 2235 . . . . 5  |-  F/_ x
( u `  w
)
4 nfof.1 . . . . 5  |-  F/_ x R
5 nfcv 2235 . . . . 5  |-  F/_ x
( v `  w
)
63, 4, 5nfbr 3911 . . . 4  |-  F/ x
( u `  w
) R ( v `
 w )
72, 6nfralxy 2425 . . 3  |-  F/ x A. w  e.  ( dom  u  i^i  dom  v
) ( u `  w ) R ( v `  w )
87nfopab 3928 . 2  |-  F/_ x { <. u ,  v
>.  |  A. w  e.  ( dom  u  i^i 
dom  v ) ( u `  w ) R ( v `  w ) }
91, 8nfcxfr 2232 1  |-  F/_ x  oR R
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2222   A.wral 2370    i^i cin 3012   class class class wbr 3867   {copab 3920   dom cdm 4467   ` cfv 5049    oRcofr 5893
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-v 2635  df-un 3017  df-sn 3472  df-pr 3473  df-op 3475  df-br 3868  df-opab 3922  df-ofr 5895
This theorem is referenced by: (None)
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