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Theorem nfbr 3836
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
StepHypRef Expression
1 nfbr.1 . . . 4  |-  F/_ x A
21a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
3 nfbr.2 . . . 4  |-  F/_ x R
43a1i 9 . . 3  |-  ( T. 
->  F/_ x R )
5 nfbr.3 . . . 4  |-  F/_ x B
65a1i 9 . . 3  |-  ( T. 
->  F/_ x B )
72, 4, 6nfbrd 3835 . 2  |-  ( T. 
->  F/ x  A R B )
87trud 1268 1  |-  F/ x  A R B
Colors of variables: wff set class
Syntax hints:   T. wtru 1260   F/wnf 1365   F/_wnfc 2181   class class class wbr 3792
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793
This theorem is referenced by:  sbcbrg  3841  nfpo  4066  nfso  4067  pofun  4077  nfse  4106  nffrfor  4113  nfwe  4120  nfco  4529  nfcnv  4542  dfdmf  4556  dfrnf  4603  nfdm  4606  dffun6f  4943  dffun4f  4946  nffv  5213  funfvdm2f  5266  fvmptss2  5275  f1ompt  5348  fmptco  5358  nfiso  5474  ofrfval2  5755  tposoprab  5926  xpcomco  6331  nfsup  6398  caucvgprprlemaddq  6864  nfsum1  10106  nfsum  10107  oddpwdclemdvds  10258  oddpwdclemndvds  10259
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