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

Theorem uneq2i 3124
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 3121 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 7 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1285  cun 2972
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978
This theorem is referenced by:  un4  3133  unundir  3135  difun2  3323  difdifdirss  3328  qdass  3491  qdassr  3492  unisuc  4170  iunsuc  4177  fmptap  5379  fvsnun1  5386  rdgival  6025  rdg0  6030  undiffi  6433  facnn  9740  fac0  9741
  Copyright terms: Public domain W3C validator