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Theorem nfov 5794
Description: Bound-variable hypothesis builder for operation value. (Contributed by NM, 4-May-2004.)
Hypotheses
Ref Expression
nfov.1  |-  F/_ x A
nfov.2  |-  F/_ x F
nfov.3  |-  F/_ x B
Assertion
Ref Expression
nfov  |-  F/_ x
( A F B )

Proof of Theorem nfov
StepHypRef Expression
1 nfov.1 . . . 4  |-  F/_ x A
21a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
3 nfov.2 . . . 4  |-  F/_ x F
43a1i 9 . . 3  |-  ( T. 
->  F/_ x F )
5 nfov.3 . . . 4  |-  F/_ x B
65a1i 9 . . 3  |-  ( T. 
->  F/_ x B )
72, 4, 6nfovd 5793 . 2  |-  ( T. 
->  F/_ x ( A F B ) )
87mptru 1340 1  |-  F/_ x
( A F B )
Colors of variables: wff set class
Syntax hints:   T. wtru 1332   F/_wnfc 2266  (class class class)co 5767
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770
This theorem is referenced by:  csbov123g  5802  ovmpos  5887  ov2gf  5888  ovmpodxf  5889  ovmpodv2  5897  ovi3  5900  nfof  5980  offval2  5990  caucvgprprlemaddq  7509  nfseq  10221  fsumadd  11168  mertenslem2  11298  oddpwdclemdvds  11837  oddpwdclemndvds  11838  cnmpt2t  12451  cnmptcom  12456  fsumcncntop  12714
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