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Theorem inteqi 3619
 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 3618 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1243  ∩ cint 3615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-int 3616 This theorem is referenced by:  elintrab  3627  ssintrab  3638  intmin2  3641  intsng  3649  intexrabim  3907  op1stb  4209  bm2.5ii  4222  dfiin3g  4590  op2ndb  4804  bj-dfom  10057  bj-omind  10058
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