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Theorem nfbr 3942
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 3941 . 2  |-  ( T. 
->  F/ x  A R B )
87mptru 1323 1  |-  F/ x  A R B
Colors of variables: wff set class
Syntax hints:   T. wtru 1315   F/wnf 1419   F/_wnfc 2243   class class class wbr 3897
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898
This theorem is referenced by:  sbcbrg  3950  nfpo  4191  nfso  4192  pofun  4202  nfse  4231  nffrfor  4238  nfwe  4245  nfco  4672  nfcnv  4686  dfdmf  4700  dfrnf  4748  nfdm  4751  dffun6f  5104  dffun4f  5107  nffv  5397  funfvdm2f  5452  fvmptss2  5462  f1ompt  5537  fmptco  5552  nfiso  5673  nfofr  5954  ofrfval2  5964  tposoprab  6143  xpcomco  6686  nfsup  6845  caucvgprprlemaddq  7480  lble  8662  nfsum1  11065  nfsum  11066  fsum00  11171  mertenslem2  11245  oddpwdclemdvds  11743  oddpwdclemndvds  11744
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