Theorem nfov 5974

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 5973	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1382	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1374   F/_wnfc 2335  (class class class)co 5944

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-uni 3851  df-br 4045  df-iota 5232  df-fv 5279  df-ov 5947

This theorem is referenced by:  csbov123g  5983  ovmpos  6069  ov2gf  6070  ovmpodxf  6071  ovmpodv2  6079  ovi3  6083  nfof  6164  offval2  6174  caucvgprprlemaddq  7821  nfseq  10602  fsumadd  11717  mertenslem2  11847  fprodrec  11940  fproddivapf  11942  oddpwdclemdvds  12492  oddpwdclemndvds  12493  pcmpt  12666  pcmptdvds  12668  cnmpt2t  14765  cnmptcom  14770  fsumcncntop  15039  dvmptfsum  15197  elplyd  15213