Theorem nfov 6079

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 6078	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1407	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1399   F/_wnfc 2371  (class class class)co 6049

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 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rex 2526  df-v 2814  df-un 3214  df-sn 3694  df-pr 3695  df-op 3697  df-uni 3914  df-br 4109  df-iota 5311  df-fv 5359  df-ov 6052

This theorem is referenced by:  csbov123g  6088  ovmpos  6176  ov2gf  6177  ovmpodxf  6178  ovmpodv2  6186  ovi3  6190  nfof  6271  offval2  6281  caucvgprprlemaddq  8022  nfseq  10818  fsumadd  12088  mertenslem2  12218  fprodrec  12311  fproddivapf  12313  oddpwdclemdvds  12863  oddpwdclemndvds  12864  pcmpt  13037  pcmptdvds  13039  cnmpt2t  15150  cnmptcom  15155  fsumcncntop  15424  dvmptfsum  15582  elplyd  15598