Theorem nfbr 4106

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 4105	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1382	1 |- F/ x A R B

Syntax hints:   T. wtru 1374   F/wnf 1484   F/_wnfc 2337   class class class wbr 4059

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650  df-op 3652  df-br 4060

This theorem is referenced by:  sbcbrg  4114  nfpo  4366  nfso  4367  pofun  4377  nfse  4406  nffrfor  4413  nfwe  4420  nfco  4861  nfcnv  4875  dfdmf  4890  dfrnf  4938  nfdm  4941  dffun6f  5303  dffun4f  5306  nffv  5609  funfvdm2f  5667  fvmptss2  5677  f1ompt  5754  fmptco  5769  nfiso  5898  nfofr  6188  ofrfval2  6198  tposoprab  6389  xpcomco  6946  nfsup  7120  caucvgprprlemaddq  7856  lble  9055  nfsum1  11782  nfsum  11783  fsum00  11888  mertenslem2  11962  nfcprod1  11980  nfcprod  11981  fprodap0  12047  fprodrec  12055  fproddivapf  12057  fprodap0f  12062  fprodle  12066  oddpwdclemdvds  12607  oddpwdclemndvds  12608