Theorem nfov 5925

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 5924	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1373	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1365   F/_wnfc 2319  (class class class)co 5895

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5898

This theorem is referenced by:  csbov123g  5933  ovmpos  6019  ov2gf  6020  ovmpodxf  6021  ovmpodv2  6029  ovi3  6032  nfof  6111  offval2  6121  caucvgprprlemaddq  7736  nfseq  10485  fsumadd  11445  mertenslem2  11575  fprodrec  11668  fproddivapf  11670  oddpwdclemdvds  12201  oddpwdclemndvds  12202  pcmpt  12374  pcmptdvds  12376  cnmpt2t  14245  cnmptcom  14250  fsumcncntop  14508