Theorem nfbr 4028

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 4027	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1352	1 |- F/ x A R B

Syntax hints:   T. wtru 1344   F/wnf 1448   F/_wnfc 2295   class class class wbr 3982

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-op 3585  df-br 3983

This theorem is referenced by:  sbcbrg  4036  nfpo  4279  nfso  4280  pofun  4290  nfse  4319  nffrfor  4326  nfwe  4333  nfco  4769  nfcnv  4783  dfdmf  4797  dfrnf  4845  nfdm  4848  dffun6f  5201  dffun4f  5204  nffv  5496  funfvdm2f  5551  fvmptss2  5561  f1ompt  5636  fmptco  5651  nfiso  5774  nfofr  6056  ofrfval2  6066  tposoprab  6248  xpcomco  6792  nfsup  6957  caucvgprprlemaddq  7649  lble  8842  nfsum1  11297  nfsum  11298  fsum00  11403  mertenslem2  11477  nfcprod1  11495  nfcprod  11496  fprodap0  11562  fprodrec  11570  fproddivapf  11572  fprodap0f  11577  fprodle  11581  oddpwdclemdvds  12102  oddpwdclemndvds  12103