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Theorem nfof 5955
Description: Hypothesis builder for function operation. (Contributed by Mario Carneiro, 20-Jul-2014.)
Hypothesis
Ref Expression
nfof.1  |-  F/_ x R
Assertion
Ref Expression
nfof  |-  F/_ x  oF R

Proof of Theorem nfof
Dummy variables  u  v  w are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-of 5950 . 2  |-  oF R  =  ( u  e.  _V ,  v  e.  _V  |->  ( w  e.  ( dom  u  i^i  dom  v )  |->  ( ( u `  w
) R ( v `
 w ) ) ) )
2 nfcv 2258 . . 3  |-  F/_ x _V
3 nfcv 2258 . . . 4  |-  F/_ x
( dom  u  i^i  dom  v )
4 nfcv 2258 . . . . 5  |-  F/_ x
( u `  w
)
5 nfof.1 . . . . 5  |-  F/_ x R
6 nfcv 2258 . . . . 5  |-  F/_ x
( v `  w
)
74, 5, 6nfov 5769 . . . 4  |-  F/_ x
( ( u `  w ) R ( v `  w ) )
83, 7nfmpt 3990 . . 3  |-  F/_ x
( w  e.  ( dom  u  i^i  dom  v )  |->  ( ( u `  w ) R ( v `  w ) ) )
92, 2, 8nfmpo 5808 . 2  |-  F/_ x
( u  e.  _V ,  v  e.  _V  |->  ( w  e.  ( dom  u  i^i  dom  v
)  |->  ( ( u `
 w ) R ( v `  w
) ) ) )
101, 9nfcxfr 2255 1  |-  F/_ x  oF R
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2245   _Vcvv 2660    i^i cin 3040    |-> cmpt 3959   dom cdm 4509   ` cfv 5093  (class class class)co 5742    e. cmpo 5744    oFcof 5948
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-opab 3960  df-mpt 3961  df-iota 5058  df-fv 5101  df-ov 5745  df-oprab 5746  df-mpo 5747  df-of 5950
This theorem is referenced by: (None)
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