Theorem nfov 6115

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 6114	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1411	1 |- F/_ x ( A F B )

This proof depends on syntax axioms:   T. wtru 1403   F/_wnfc 2379  (class class class)co 6085

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-un 3224  df-sn 3715  df-pr 3716  df-op 3718  df-uni 3936  df-br 4131  df-iota 5337  df-fv 5385  df-ov 6088

This theorem is used by:  csbov123g  6124  ovmpos  6212  ov2gf  6213  ovmpodxf  6214  ovmpodv2  6222  ovi3  6226  nfof  6308  offval2  6318  caucvgprprlemaddq  8075  nfseq  10894  fsumadd  12173  mertenslem2  12303  fprodrec  12396  fproddivapf  12398  oddpwdclemdvds  12948  oddpwdclemndvds  12949  pcmpt  13122  pcmptdvds  13124  gsummptfidmadd  14161  cnmpt2t  15394  cnmptcom  15399  fsumcncntop  15668  dvmptfsum  15826  elplyd  15842