Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  uneq2i GIF version

Theorem uneq2i 3227
 Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
uneq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem uneq2i
StepHypRef Expression
1 uneq1i.1 . 2 𝐴 = 𝐵
2 uneq2 3224 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ∪ cun 3069 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-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 This theorem is referenced by:  un4  3236  unundir  3238  difun2  3442  difdifdirss  3447  qdass  3620  qdassr  3621  unisuc  4335  iunsuc  4342  fmptap  5610  fvsnun1  5617  rdgival  6279  rdg0  6284  undifdc  6812  exmidfodomrlemim  7057  djuassen  7073  facnn  10480  fac0  10481  fsum2dlemstep  11210  fsumiun  11253
 Copyright terms: Public domain W3C validator