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Theorem eqimss2 3156
Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
eqimss2 (𝐵 = 𝐴𝐴𝐵)

Proof of Theorem eqimss2
StepHypRef Expression
1 eqimss 3155 . 2 (𝐴 = 𝐵𝐴𝐵)
21eqcoms 2143 1 (𝐵 = 𝐴𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  wss 3075
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3081  df-ss 3088
This theorem is referenced by:  disjeq2  3917  disjeq1  3920  poeq2  4229  seeq1  4268  seeq2  4269  dmcoeq  4818  xp11m  4984  funeq  5150  fconst3m  5646  tposeq  6151  undifdcss  6818  ennnfonelemk  11947  ennnfonelemss  11957  qnnen  11978  topgele  12233  topontopn  12241  txdis  12483
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