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Theorem eqimssi 3080
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 3044 . 2 𝐴𝐴
2 eqimssi.1 . 2 𝐴 = 𝐵
31, 2sseqtri 3058 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1289  wss 2999
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-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012
This theorem is referenced by:  funi  5046  fpr  5479  elfzo1  9601  sumsplitdc  10826  isumlessdc  10890
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