ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  uneq1i GIF version

Theorem uneq1i 3150
Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
uneq1i (𝐴𝐶) = (𝐵𝐶)

Proof of Theorem uneq1i
StepHypRef Expression
1 uneq1i.1 . 2 𝐴 = 𝐵
2 uneq1 3147 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1289  cun 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003
This theorem is referenced by:  un12  3158  unundi  3161  tpcoma  3536  qdass  3539  qdassr  3540  tpidm12  3541  resasplitss  5190  fmptpr  5489  df2o3  6195  undifdc  6634  sbthlemi6  6671  exmidfodomrlemim  6827  znnen  11489  setscom  11534
  Copyright terms: Public domain W3C validator