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Theorem nfbr 3799
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 xA
nfbr.2 x𝑅
nfbr.3 xB
Assertion
Ref Expression
nfbr x A𝑅B

Proof of Theorem nfbr
StepHypRef Expression
1 nfbr.1 . . . 4 xA
21a1i 9 . . 3 ( ⊤ → xA)
3 nfbr.2 . . . 4 x𝑅
43a1i 9 . . 3 ( ⊤ → x𝑅)
5 nfbr.3 . . . 4 xB
65a1i 9 . . 3 ( ⊤ → xB)
72, 4, 6nfbrd 3798 . 2 ( ⊤ → Ⅎx A𝑅B)
87trud 1251 1 x A𝑅B
Colors of variables: wff set class
Syntax hints:  wtru 1243  wnf 1346  wnfc 2162   class class class wbr 3755
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756
This theorem is referenced by:  sbcbrg  3804  nfpo  4029  nfso  4030  pofun  4040  nfse  4063  nfco  4444  nfcnv  4457  dfdmf  4471  dfrnf  4518  nfdm  4521  dffun6f  4858  dffun4f  4861  nffv  5128  funfvdm2f  5181  fvmptss2  5190  f1ompt  5263  fmptco  5273  nfiso  5389  ofrfval2  5669  tposoprab  5836  xpcomco  6236
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