Theorem nfbr 4075

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 4074	. 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 4029

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 3157  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030

This theorem is referenced by:  sbcbrg  4083  nfpo  4332  nfso  4333  pofun  4343  nfse  4372  nffrfor  4379  nfwe  4386  nfco  4827  nfcnv  4841  dfdmf  4855  dfrnf  4903  nfdm  4906  dffun6f  5267  dffun4f  5270  nffv  5564  funfvdm2f  5622  fvmptss2  5632  f1ompt  5709  fmptco  5724  nfiso  5849  nfofr  6137  ofrfval2  6147  tposoprab  6333  xpcomco  6880  nfsup  7051  caucvgprprlemaddq  7768  lble  8966  nfsum1  11499  nfsum  11500  fsum00  11605  mertenslem2  11679  nfcprod1  11697  nfcprod  11698  fprodap0  11764  fprodrec  11772  fproddivapf  11774  fprodap0f  11779  fprodle  11783  oddpwdclemdvds  12308  oddpwdclemndvds  12309