Theorem nfbr 3982

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 3981	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1341	1 |- F/ x A R B

Syntax hints:   T. wtru 1333   F/wnf 1437   F/_wnfc 2269   class class class wbr 3937

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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-sn 3538  df-pr 3539  df-op 3541  df-br 3938

This theorem is referenced by:  sbcbrg  3990  nfpo  4231  nfso  4232  pofun  4242  nfse  4271  nffrfor  4278  nfwe  4285  nfco  4712  nfcnv  4726  dfdmf  4740  dfrnf  4788  nfdm  4791  dffun6f  5144  dffun4f  5147  nffv  5439  funfvdm2f  5494  fvmptss2  5504  f1ompt  5579  fmptco  5594  nfiso  5715  nfofr  5996  ofrfval2  6006  tposoprab  6185  xpcomco  6728  nfsup  6887  caucvgprprlemaddq  7540  lble  8729  nfsum1  11157  nfsum  11158  fsum00  11263  mertenslem2  11337  nfcprod1  11355  nfcprod  11356  oddpwdclemdvds  11884  oddpwdclemndvds  11885