Theorem nfov 5952

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 5951	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1373	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1365   F/_wnfc 2326  (class class class)co 5922

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-op 3631  df-uni 3840  df-br 4034  df-iota 5219  df-fv 5266  df-ov 5925

This theorem is referenced by:  csbov123g  5960  ovmpos  6046  ov2gf  6047  ovmpodxf  6048  ovmpodv2  6056  ovi3  6060  nfof  6141  offval2  6151  caucvgprprlemaddq  7775  nfseq  10549  fsumadd  11571  mertenslem2  11701  fprodrec  11794  fproddivapf  11796  oddpwdclemdvds  12338  oddpwdclemndvds  12339  pcmpt  12512  pcmptdvds  12514  cnmpt2t  14529  cnmptcom  14534  fsumcncntop  14803  dvmptfsum  14961  elplyd  14977