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

Theorem uneq2i 3140
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  |-  ( C  u.  A )  =  ( C  u.  B
)

Proof of Theorem uneq2i
StepHypRef Expression
1 uneq1i.1 . 2  |-  A  =  B
2 uneq2 3137 . 2  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
31, 2ax-mp 7 1  |-  ( C  u.  A )  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1287    u. cun 2986
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992
This theorem is referenced by:  un4  3149  unundir  3151  difun2  3349  difdifdirss  3354  qdass  3522  qdassr  3523  unisuc  4213  iunsuc  4220  fmptap  5444  fvsnun1  5451  rdgival  6095  rdg0  6100  undifdc  6580  exmidfodomrlemim  6764  facnn  10024  fac0  10025
  Copyright terms: Public domain W3C validator