Theorem nfov 6058

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 6057	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1407	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1399   F/_wnfc 2362  (class class class)co 6028

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 2213

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-op 3682  df-uni 3899  df-br 4094  df-iota 5293  df-fv 5341  df-ov 6031

This theorem is referenced by:  csbov123g  6067  ovmpos  6155  ov2gf  6156  ovmpodxf  6157  ovmpodv2  6165  ovi3  6169  nfof  6250  offval2  6260  caucvgprprlemaddq  7988  nfseq  10782  fsumadd  12047  mertenslem2  12177  fprodrec  12270  fproddivapf  12272  oddpwdclemdvds  12822  oddpwdclemndvds  12823  pcmpt  12996  pcmptdvds  12998  cnmpt2t  15104  cnmptcom  15109  fsumcncntop  15378  dvmptfsum  15536  elplyd  15552