Theorem nfov 6031

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

Step	Hyp	Ref	Expression
1		nfov.1	. . . 4 |- F/_ x A
2	1	a1i 9	. . 3 |- ( T. -> F/_ x A )
3		nfov.2	. . . 4 |- F/_ x F
4	3	a1i 9	. . 3 |- ( T. -> F/_ x F )
5		nfov.3	. . . 4 |- F/_ x B
6	5	a1i 9	. . 3 |- ( T. -> F/_ x B )
7	2, 4, 6	nfovd 6030	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1404	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1396   F/_wnfc 2359  (class class class)co 6001

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-v 2801  df-un 3201  df-sn 3672  df-pr 3673  df-op 3675  df-uni 3889  df-br 4084  df-iota 5278  df-fv 5326  df-ov 6004

This theorem is referenced by:  csbov123g  6040  ovmpos  6128  ov2gf  6129  ovmpodxf  6130  ovmpodv2  6138  ovi3  6142  nfof  6224  offval2  6234  caucvgprprlemaddq  7895  nfseq  10679  fsumadd  11917  mertenslem2  12047  fprodrec  12140  fproddivapf  12142  oddpwdclemdvds  12692  oddpwdclemndvds  12693  pcmpt  12866  pcmptdvds  12868  cnmpt2t  14967  cnmptcom  14972  fsumcncntop  15241  dvmptfsum  15399  elplyd  15415