Theorem nfov 5997

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 5996	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1382	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1374   F/_wnfc 2337  (class class class)co 5967

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rex 2492  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650  df-op 3652  df-uni 3865  df-br 4060  df-iota 5251  df-fv 5298  df-ov 5970

This theorem is referenced by:  csbov123g  6006  ovmpos  6092  ov2gf  6093  ovmpodxf  6094  ovmpodv2  6102  ovi3  6106  nfof  6187  offval2  6197  caucvgprprlemaddq  7856  nfseq  10639  fsumadd  11832  mertenslem2  11962  fprodrec  12055  fproddivapf  12057  oddpwdclemdvds  12607  oddpwdclemndvds  12608  pcmpt  12781  pcmptdvds  12783  cnmpt2t  14880  cnmptcom  14885  fsumcncntop  15154  dvmptfsum  15312  elplyd  15328