Theorem nfbr 4135

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 4134	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1406	1 |- F/ x A R B

Syntax hints:   T. wtru 1398   F/wnf 1508   F/_wnfc 2361   class class class wbr 4088

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676  df-op 3678  df-br 4089

This theorem is referenced by:  sbcbrg  4143  nfpo  4398  nfso  4399  pofun  4409  nfse  4438  nffrfor  4445  nfwe  4452  nfco  4895  nfcnv  4909  dfdmf  4924  dfrnf  4973  nfdm  4976  dffun6f  5339  dffun4f  5342  nffv  5649  funfvdm2f  5711  fvmptss2  5721  f1ompt  5798  fmptco  5813  nfiso  5947  nfofr  6242  ofrfval2  6252  tposoprab  6446  modom  6994  xpcomco  7010  nfsup  7191  caucvgprprlemaddq  7928  lble  9127  nfsum1  11934  nfsum  11935  fsum00  12041  mertenslem2  12115  nfcprod1  12133  nfcprod  12134  fprodap0  12200  fprodrec  12208  fproddivapf  12210  fprodap0f  12215  fprodle  12219  oddpwdclemdvds  12760  oddpwdclemndvds  12761