Theorem nfov 5976

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 5975	. 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 5946

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 4046  df-iota 5233  df-fv 5280  df-ov 5949

This theorem is referenced by:  csbov123g  5985  ovmpos  6071  ov2gf  6072  ovmpodxf  6073  ovmpodv2  6081  ovi3  6085  nfof  6166  offval2  6176  caucvgprprlemaddq  7823  nfseq  10604  fsumadd  11750  mertenslem2  11880  fprodrec  11973  fproddivapf  11975  oddpwdclemdvds  12525  oddpwdclemndvds  12526  pcmpt  12699  pcmptdvds  12701  cnmpt2t  14798  cnmptcom  14803  fsumcncntop  15072  dvmptfsum  15230  elplyd  15246