Theorem nfbr 4161

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 4160	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1407	1 |- F/ x A R B

Syntax hints:   T. wtru 1399   F/wnf 1509   F/_wnfc 2373   class class class wbr 4114

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-un 3218  df-sn 3700  df-pr 3701  df-op 3703  df-br 4115

This theorem is referenced by:  sbcbrg  4169  nfpo  4427  nfso  4428  pofun  4438  nfse  4467  nffrfor  4474  nfwe  4481  nfco  4925  nfcnv  4939  dfdmf  4954  dfrnf  5003  nfdm  5006  dffun6f  5370  dffun4f  5373  nffv  5685  funfvdm2f  5747  fvmptss2  5757  f1ompt  5833  fmptco  5848  nfiso  5985  nfofr  6282  ofrfval2  6292  tposoprab  6524  modom  7074  xpcomco  7090  nfsup  7296  caucvgprprlemaddq  8039  lble  9238  nfsum1  12066  nfsum  12067  fsum00  12173  mertenslem2  12247  nfcprod1  12265  nfcprod  12266  fprodap0  12332  fprodrec  12340  fproddivapf  12342  fprodap0f  12347  fprodle  12351  oddpwdclemdvds  12892  oddpwdclemndvds  12893