Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfbr GIF version

Theorem nfbr 3835
 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 3834 . 2 (⊤ → Ⅎ𝑥 𝐴𝑅𝐵)
87trud 1268 1 𝑥 𝐴𝑅𝐵
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1260  Ⅎwnf 1365  Ⅎwnfc 2181   class class class wbr 3791 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 2949  df-sn 3408  df-pr 3409  df-op 3411  df-br 3792 This theorem is referenced by:  sbcbrg  3840  nfpo  4065  nfso  4066  pofun  4076  nfse  4105  nffrfor  4112  nfwe  4119  nfco  4528  nfcnv  4541  dfdmf  4555  dfrnf  4602  nfdm  4605  dffun6f  4942  dffun4f  4945  nffv  5212  funfvdm2f  5265  fvmptss2  5274  f1ompt  5347  fmptco  5357  nfiso  5473  ofrfval2  5754  tposoprab  5925  xpcomco  6330  nfsup  6397  caucvgprprlemaddq  6863  nfsum1  10098  nfsum  10099  oddpwdclemdvds  10230  oddpwdclemndvds  10231
 Copyright terms: Public domain W3C validator