Theorem nfbr 4076

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 4075	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1373	1 |- F/ x A R B

Syntax hints:   T. wtru 1365   F/wnf 1471   F/_wnfc 2323   class class class wbr 4030

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3158  df-sn 3625  df-pr 3626  df-op 3628  df-br 4031

This theorem is referenced by:  sbcbrg  4084  nfpo  4333  nfso  4334  pofun  4344  nfse  4373  nffrfor  4380  nfwe  4387  nfco  4828  nfcnv  4842  dfdmf  4856  dfrnf  4904  nfdm  4907  dffun6f  5268  dffun4f  5271  nffv  5565  funfvdm2f  5623  fvmptss2  5633  f1ompt  5710  fmptco  5725  nfiso  5850  nfofr  6139  ofrfval2  6149  tposoprab  6335  xpcomco  6882  nfsup  7053  caucvgprprlemaddq  7770  lble  8968  nfsum1  11502  nfsum  11503  fsum00  11608  mertenslem2  11682  nfcprod1  11700  nfcprod  11701  fprodap0  11767  fprodrec  11775  fproddivapf  11777  fprodap0f  11782  fprodle  11786  oddpwdclemdvds  12311  oddpwdclemndvds  12312