Theorem nfbr 3808

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 3807	. 2 |- ( T. -> F/ x A R B )
8	7	trud 1252	1 |- F/ x A R B

Syntax hints:   T. wtru 1244   F/wnf 1349   F/_wnfc 2165   class class class wbr 3764

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765

This theorem is referenced by:  sbcbrg  3813  nfpo  4038  nfso  4039  pofun  4049  nfse  4078  nffrfor  4085  nfwe  4092  nfco  4501  nfcnv  4514  dfdmf  4528  dfrnf  4575  nfdm  4578  dffun6f  4915  dffun4f  4918  nffv  5185  funfvdm2f  5238  fvmptss2  5247  f1ompt  5320  fmptco  5330  nfiso  5446  ofrfval2  5727  tposoprab  5895  xpcomco  6300  caucvgprprlemaddq  6806  nfsum1  9875  nfsum  9876