Theorem nfov 6088

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 6087	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1407	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1399   F/_wnfc 2373  (class class class)co 6058

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rex 2528  df-v 2817  df-un 3218  df-sn 3700  df-pr 3701  df-op 3703  df-uni 3920  df-br 4115  df-iota 5317  df-fv 5365  df-ov 6061

This theorem is referenced by:  csbov123g  6097  ovmpos  6185  ov2gf  6186  ovmpodxf  6187  ovmpodv2  6195  ovi3  6199  nfof  6281  offval2  6291  caucvgprprlemaddq  8039  nfseq  10843  fsumadd  12117  mertenslem2  12247  fprodrec  12340  fproddivapf  12342  oddpwdclemdvds  12892  oddpwdclemndvds  12893  pcmpt  13066  pcmptdvds  13068  cnmpt2t  15284  cnmptcom  15289  fsumcncntop  15558  dvmptfsum  15716  elplyd  15732