Theorem nfbr 3895

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 3894	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1299	1 |- F/ x A R B

Syntax hints:   T. wtru 1291   F/wnf 1395   F/_wnfc 2216   class class class wbr 3851

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-un 3004  df-sn 3456  df-pr 3457  df-op 3459  df-br 3852

This theorem is referenced by:  sbcbrg  3900  nfpo  4137  nfso  4138  pofun  4148  nfse  4177  nffrfor  4184  nfwe  4191  nfco  4614  nfcnv  4628  dfdmf  4642  dfrnf  4689  nfdm  4692  dffun6f  5041  dffun4f  5044  nffv  5328  funfvdm2f  5382  fvmptss2  5392  f1ompt  5464  fmptco  5478  nfiso  5599  nfofr  5876  ofrfval2  5885  tposoprab  6059  xpcomco  6596  nfsup  6741  caucvgprprlemaddq  7328  lble  8469  nfsum1  10806  nfsum  10807  fsum00  10917  mertenslem2  10991  oddpwdclemdvds  11487  oddpwdclemndvds  11488