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Theorem eqimssi 2999
 Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1 𝐴 = 𝐵
Assertion
Ref Expression
eqimssi 𝐴𝐵

Proof of Theorem eqimssi
StepHypRef Expression
1 ssid 2964 . 2 𝐴𝐴
2 eqimssi.1 . 2 𝐴 = 𝐵
31, 2sseqtri 2977 1 𝐴𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ⊆ wss 2917 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  funi  4932  fpr  5345  elfzo1  9046
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