Theorem nfbr 4130

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 4129	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1404	1 |- F/ x A R B

Syntax hints:   T. wtru 1396   F/wnf 1506   F/_wnfc 2359   class class class wbr 4083

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-sn 3672  df-pr 3673  df-op 3675  df-br 4084

This theorem is referenced by:  sbcbrg  4138  nfpo  4392  nfso  4393  pofun  4403  nfse  4432  nffrfor  4439  nfwe  4446  nfco  4887  nfcnv  4901  dfdmf  4916  dfrnf  4965  nfdm  4968  dffun6f  5331  dffun4f  5334  nffv  5639  funfvdm2f  5701  fvmptss2  5711  f1ompt  5788  fmptco  5803  nfiso  5936  nfofr  6231  ofrfval2  6241  tposoprab  6432  xpcomco  6993  nfsup  7170  caucvgprprlemaddq  7906  lble  9105  nfsum1  11883  nfsum  11884  fsum00  11989  mertenslem2  12063  nfcprod1  12081  nfcprod  12082  fprodap0  12148  fprodrec  12156  fproddivapf  12158  fprodap0f  12163  fprodle  12167  oddpwdclemdvds  12708  oddpwdclemndvds  12709