Theorem nfbr 4140

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 4139	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1407	1 |- F/ x A R B

Syntax hints:   T. wtru 1399   F/wnf 1509   F/_wnfc 2362   class class class wbr 4093

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-op 3682  df-br 4094

This theorem is referenced by:  sbcbrg  4148  nfpo  4404  nfso  4405  pofun  4415  nfse  4444  nffrfor  4451  nfwe  4458  nfco  4901  nfcnv  4915  dfdmf  4930  dfrnf  4979  nfdm  4982  dffun6f  5346  dffun4f  5349  nffv  5658  funfvdm2f  5720  fvmptss2  5730  f1ompt  5806  fmptco  5821  nfiso  5957  nfofr  6251  ofrfval2  6261  tposoprab  6489  modom  7037  xpcomco  7053  nfsup  7251  caucvgprprlemaddq  7988  lble  9186  nfsum1  11996  nfsum  11997  fsum00  12103  mertenslem2  12177  nfcprod1  12195  nfcprod  12196  fprodap0  12262  fprodrec  12270  fproddivapf  12272  fprodap0f  12277  fprodle  12281  oddpwdclemdvds  12822  oddpwdclemndvds  12823