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Theorem inteqi 3675
Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqi.1 𝐴 = 𝐵
Assertion
Ref Expression
inteqi 𝐴 = 𝐵

Proof of Theorem inteqi
StepHypRef Expression
1 inteqi.1 . 2 𝐴 = 𝐵
2 inteq 3674 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1287   cint 3671
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-ral 2360  df-int 3672
This theorem is referenced by:  elintrab  3683  ssintrab  3694  intmin2  3697  intsng  3705  intexrabim  3964  op1stb  4273  bm2.5ii  4286  dfiin3g  4659  op2ndb  4880  bj-dfom  11266  bj-omind  11267
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