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Theorem nfbr 4049
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 4048 . 2 (⊤ → Ⅎ𝑥 𝐴𝑅𝐵)
87mptru 1362 1 𝑥 𝐴𝑅𝐵
Colors of variables: wff set class
Syntax hints:  wtru 1354  wnf 1460  wnfc 2306   class class class wbr 4003
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-sn 3598  df-pr 3599  df-op 3601  df-br 4004
This theorem is referenced by:  sbcbrg  4057  nfpo  4301  nfso  4302  pofun  4312  nfse  4341  nffrfor  4348  nfwe  4355  nfco  4792  nfcnv  4806  dfdmf  4820  dfrnf  4868  nfdm  4871  dffun6f  5229  dffun4f  5232  nffv  5525  funfvdm2f  5581  fvmptss2  5591  f1ompt  5667  fmptco  5682  nfiso  5806  nfofr  6088  ofrfval2  6098  tposoprab  6280  xpcomco  6825  nfsup  6990  caucvgprprlemaddq  7706  lble  8903  nfsum1  11363  nfsum  11364  fsum00  11469  mertenslem2  11543  nfcprod1  11561  nfcprod  11562  fprodap0  11628  fprodrec  11636  fproddivapf  11638  fprodap0f  11643  fprodle  11647  oddpwdclemdvds  12169  oddpwdclemndvds  12170
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