Theorem nfbr 4080

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 4079	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1373	1 |- F/ x A R B

Syntax hints:   T. wtru 1365   F/wnf 1474   F/_wnfc 2326   class class class wbr 4034

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-sn 3629  df-pr 3630  df-op 3632  df-br 4035

This theorem is referenced by:  sbcbrg  4088  nfpo  4337  nfso  4338  pofun  4348  nfse  4377  nffrfor  4384  nfwe  4391  nfco  4832  nfcnv  4846  dfdmf  4860  dfrnf  4908  nfdm  4911  dffun6f  5272  dffun4f  5275  nffv  5571  funfvdm2f  5629  fvmptss2  5639  f1ompt  5716  fmptco  5731  nfiso  5856  nfofr  6146  ofrfval2  6156  tposoprab  6347  xpcomco  6894  nfsup  7067  caucvgprprlemaddq  7792  lble  8991  nfsum1  11538  nfsum  11539  fsum00  11644  mertenslem2  11718  nfcprod1  11736  nfcprod  11737  fprodap0  11803  fprodrec  11811  fproddivapf  11813  fprodap0f  11818  fprodle  11822  oddpwdclemdvds  12363  oddpwdclemndvds  12364