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Theorem eqimss2 2975
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 2974 . 2 (A = BAB)
21eqcoms 2025 1 (B = AAB)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228  wss 2894
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-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  disjeq2  3723  disjeq1  3726  poeq2  4011  seeq1  4044  seeq2  4045  dmcoeq  4531  xp11m  4686  funeq  4847  fconst3m  5305  tposeq  5784
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