Theorem nfbr 3829

Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 14-Oct-2016.)

Hypotheses

Ref	Expression
nfbr.1	|- F/_ x A
nfbr.2	|- F/_ x R
nfbr.3	|- F/_ x B

Assertion

Ref	Expression
nfbr	|- F/ x A R B

Proof of Theorem nfbr

Step	Hyp	Ref	Expression
1		nfbr.1	. . . 4 |- F/_ x A
2	1	a1i 9	. . 3 |- ( T. -> F/_ x A )
3		nfbr.2	. . . 4 |- F/_ x R
4	3	a1i 9	. . 3 |- ( T. -> F/_ x R )
5		nfbr.3	. . . 4 |- F/_ x B
6	5	a1i 9	. . 3 |- ( T. -> F/_ x B )
7	2, 4, 6	nfbrd 3828	. 2 |- ( T. -> F/ x A R B )
8	7	trud 1293	1 |- F/ x A R B

Syntax hints:   T. wtru 1285   F/wnf 1389   F/_wnfc 2206   class class class wbr 3785

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-br 3786

This theorem is referenced by:  sbcbrg  3834  nfpo  4056  nfso  4057  pofun  4067  nfse  4096  nffrfor  4103  nfwe  4110  nfco  4519  nfcnv  4532  dfdmf  4546  dfrnf  4593  nfdm  4596  dffun6f  4935  dffun4f  4938  nffv  5205  funfvdm2f  5259  fvmptss2  5268  f1ompt  5341  fmptco  5351  nfiso  5466  ofrfval2  5747  tposoprab  5918  xpcomco  6323  nfsup  6405  caucvgprprlemaddq  6898  lble  8025  nfsum1  10193  nfsum  10194  oddpwdclemdvds  10548  oddpwdclemndvds  10549