ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  uneq1d GIF version

Theorem uneq1d 3197
Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998.)
Hypothesis
Ref Expression
uneq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
uneq1d (𝜑 → (𝐴𝐶) = (𝐵𝐶))

Proof of Theorem uneq1d
StepHypRef Expression
1 uneq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 uneq1 3191 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶) = (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1314  cun 3037
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-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
This theorem is referenced by:  ifeq1  3445  preq1  3568  tpeq1  3577  tpeq2  3578  resasplitss  5270  fmptpr  5578  funresdfunsnss  5589  rdgisucinc  6248  oasuc  6326  omsuc  6334  funresdfunsndc  6368  fisseneq  6786  sbthlemi5  6815  exmidfodomrlemim  7021  fzpred  9790  fseq1p1m1  9814  nn0split  9853  nnsplit  9854  fzo0sn0fzo1  9938  fzosplitprm1  9951  fsum1p  11127  zsupcllemstep  11534  setsvala  11885  setsabsd  11893  setscom  11894
  Copyright terms: Public domain W3C validator