Theorem nfov 5955

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 5954	. 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 5925

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 3629  df-pr 3630  df-op 3632  df-uni 3841  df-br 4035  df-iota 5220  df-fv 5267  df-ov 5928

This theorem is referenced by:  csbov123g  5964  ovmpos  6050  ov2gf  6051  ovmpodxf  6052  ovmpodv2  6060  ovi3  6064  nfof  6145  offval2  6155  caucvgprprlemaddq  7792  nfseq  10566  fsumadd  11588  mertenslem2  11718  fprodrec  11811  fproddivapf  11813  oddpwdclemdvds  12363  oddpwdclemndvds  12364  pcmpt  12537  pcmptdvds  12539  cnmpt2t  14613  cnmptcom  14618  fsumcncntop  14887  dvmptfsum  15045  elplyd  15061