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  5637  funfvdm2f  5699  fvmptss2  5709  f1ompt  5786  fmptco  5801  nfiso  5930  nfofr  6225  ofrfval2  6235  tposoprab  6426  xpcomco  6985  nfsup  7159  caucvgprprlemaddq  7895  lble  9094  nfsum1  11867  nfsum  11868  fsum00  11973  mertenslem2  12047  nfcprod1  12065  nfcprod  12066  fprodap0  12132  fprodrec  12140  fproddivapf  12142  fprodap0f  12147  fprodle  12151  oddpwdclemdvds  12692  oddpwdclemndvds  12693