Theorem nfov 6080

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 6079	. 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 6050

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 2815  df-un 3215  df-sn 3695  df-pr 3696  df-op 3698  df-uni 3915  df-br 4110  df-iota 5312  df-fv 5360  df-ov 6053

This theorem is referenced by:  csbov123g  6089  ovmpos  6177  ov2gf  6178  ovmpodxf  6179  ovmpodv2  6187  ovi3  6191  nfof  6272  offval2  6282  caucvgprprlemaddq  8023  nfseq  10819  fsumadd  12092  mertenslem2  12222  fprodrec  12315  fproddivapf  12317  oddpwdclemdvds  12867  oddpwdclemndvds  12868  pcmpt  13041  pcmptdvds  13043  cnmpt2t  15158  cnmptcom  15163  fsumcncntop  15432  dvmptfsum  15590  elplyd  15606