Theorem nfov 6105

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 6104	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1411	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1403   F/_wnfc 2379  (class class class)co 6075

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 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 theorem 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 3711  df-pr 3712  df-op 3714  df-uni 3931  df-br 4126  df-iota 5332  df-fv 5380  df-ov 6078

This theorem is referenced by:  csbov123g  6114  ovmpos  6202  ov2gf  6203  ovmpodxf  6204  ovmpodv2  6212  ovi3  6216  nfof  6298  offval2  6308  caucvgprprlemaddq  8065  nfseq  10872  fsumadd  12151  mertenslem2  12281  fprodrec  12374  fproddivapf  12376  oddpwdclemdvds  12926  oddpwdclemndvds  12927  pcmpt  13100  pcmptdvds  13102  gsummptfidmadd  14138  cnmpt2t  15317  cnmptcom  15322  fsumcncntop  15591  dvmptfsum  15749  elplyd  15765