Theorem nfov 5949

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 5948	. 2 |- ( T. -> F/_ x ( A F B ) )
8	7	mptru 1373	1 |- F/_ x ( A F B )

Syntax hints:   T. wtru 1365   F/_wnfc 2323  (class class class)co 5919

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-v 2762  df-un 3158  df-sn 3625  df-pr 3626  df-op 3628  df-uni 3837  df-br 4031  df-iota 5216  df-fv 5263  df-ov 5922

This theorem is referenced by:  csbov123g  5957  ovmpos  6043  ov2gf  6044  ovmpodxf  6045  ovmpodv2  6053  ovi3  6057  nfof  6138  offval2  6148  caucvgprprlemaddq  7770  nfseq  10531  fsumadd  11552  mertenslem2  11682  fprodrec  11775  fproddivapf  11777  oddpwdclemdvds  12311  oddpwdclemndvds  12312  pcmpt  12484  pcmptdvds  12486  cnmpt2t  14472  cnmptcom  14477  fsumcncntop  14746  dvmptfsum  14904  elplyd  14920