Theorem nfbr 3969

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 3968	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1340	1 |- F/ x A R B

Syntax hints:   T. wtru 1332   F/wnf 1436   F/_wnfc 2266   class class class wbr 3924

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925

This theorem is referenced by:  sbcbrg  3977  nfpo  4218  nfso  4219  pofun  4229  nfse  4258  nffrfor  4265  nfwe  4272  nfco  4699  nfcnv  4713  dfdmf  4727  dfrnf  4775  nfdm  4778  dffun6f  5131  dffun4f  5134  nffv  5424  funfvdm2f  5479  fvmptss2  5489  f1ompt  5564  fmptco  5579  nfiso  5700  nfofr  5981  ofrfval2  5991  tposoprab  6170  xpcomco  6713  nfsup  6872  caucvgprprlemaddq  7509  lble  8698  nfsum1  11118  nfsum  11119  fsum00  11224  mertenslem2  11298  nfcprod1  11316  nfcprod  11317  oddpwdclemdvds  11837  oddpwdclemndvds  11838