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Theorem uneq2i 3133
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 3130 . 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 1285    u. cun 2980
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 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986
This theorem is referenced by:  un4  3142  unundir  3144  difun2  3338  difdifdirss  3343  qdass  3507  qdassr  3508  unisuc  4196  iunsuc  4203  fmptap  5406  fvsnun1  5413  rdgival  6052  rdg0  6057  undifdc  6469  facnn  9821  fac0  9822
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