Theorem nfbr 4051

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 4050	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1362	1 |- F/ x A R B

Syntax hints:   T. wtru 1354   F/wnf 1460   F/_wnfc 2306   class class class wbr 4005

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135  df-sn 3600  df-pr 3601  df-op 3603  df-br 4006

This theorem is referenced by:  sbcbrg  4059  nfpo  4303  nfso  4304  pofun  4314  nfse  4343  nffrfor  4350  nfwe  4357  nfco  4794  nfcnv  4808  dfdmf  4822  dfrnf  4870  nfdm  4873  dffun6f  5231  dffun4f  5234  nffv  5527  funfvdm2f  5584  fvmptss2  5594  f1ompt  5670  fmptco  5685  nfiso  5810  nfofr  6092  ofrfval2  6102  tposoprab  6284  xpcomco  6829  nfsup  6994  caucvgprprlemaddq  7710  lble  8907  nfsum1  11367  nfsum  11368  fsum00  11473  mertenslem2  11547  nfcprod1  11565  nfcprod  11566  fprodap0  11632  fprodrec  11640  fproddivapf  11642  fprodap0f  11647  fprodle  11651  oddpwdclemdvds  12173  oddpwdclemndvds  12174