Theorem nfov 6037

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 6036	. 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 6007

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 6010

This theorem is referenced by:  csbov123g  6046  ovmpos  6134  ov2gf  6135  ovmpodxf  6136  ovmpodv2  6144  ovi3  6148  nfof  6230  offval2  6240  caucvgprprlemaddq  7906  nfseq  10691  fsumadd  11933  mertenslem2  12063  fprodrec  12156  fproddivapf  12158  oddpwdclemdvds  12708  oddpwdclemndvds  12709  pcmpt  12882  pcmptdvds  12884  cnmpt2t  14983  cnmptcom  14988  fsumcncntop  15257  dvmptfsum  15415  elplyd  15431