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Theorem nfbr 3974
 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 3973 . 2 (⊤ → Ⅎ𝑥 𝐴𝑅𝐵)
87mptru 1340 1 𝑥 𝐴𝑅𝐵
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1332  Ⅎwnf 1436  Ⅎwnfc 2268   class class class wbr 3929 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930 This theorem is referenced by:  sbcbrg  3982  nfpo  4223  nfso  4224  pofun  4234  nfse  4263  nffrfor  4270  nfwe  4277  nfco  4704  nfcnv  4718  dfdmf  4732  dfrnf  4780  nfdm  4783  dffun6f  5136  dffun4f  5139  nffv  5431  funfvdm2f  5486  fvmptss2  5496  f1ompt  5571  fmptco  5586  nfiso  5707  nfofr  5988  ofrfval2  5998  tposoprab  6177  xpcomco  6720  nfsup  6879  caucvgprprlemaddq  7516  lble  8705  nfsum1  11125  nfsum  11126  fsum00  11231  mertenslem2  11305  nfcprod1  11323  nfcprod  11324  oddpwdclemdvds  11848  oddpwdclemndvds  11849
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