Theorem nfbr 4035

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 4034	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1357	1 |- F/ x A R B

Syntax hints:   T. wtru 1349   F/wnf 1453   F/_wnfc 2299   class class class wbr 3989

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-br 3990

This theorem is referenced by:  sbcbrg  4043  nfpo  4286  nfso  4287  pofun  4297  nfse  4326  nffrfor  4333  nfwe  4340  nfco  4776  nfcnv  4790  dfdmf  4804  dfrnf  4852  nfdm  4855  dffun6f  5211  dffun4f  5214  nffv  5506  funfvdm2f  5561  fvmptss2  5571  f1ompt  5647  fmptco  5662  nfiso  5785  nfofr  6067  ofrfval2  6077  tposoprab  6259  xpcomco  6804  nfsup  6969  caucvgprprlemaddq  7670  lble  8863  nfsum1  11319  nfsum  11320  fsum00  11425  mertenslem2  11499  nfcprod1  11517  nfcprod  11518  fprodap0  11584  fprodrec  11592  fproddivapf  11594  fprodap0f  11599  fprodle  11603  oddpwdclemdvds  12124  oddpwdclemndvds  12125