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Theorem eqimss2i 3055
Description: Infer subclass relationship from equality. (Contributed by NM, 7-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1  |-  A  =  B
Assertion
Ref Expression
eqimss2i  |-  B  C_  A

Proof of Theorem eqimss2i
StepHypRef Expression
1 ssid 3019 . 2  |-  B  C_  B
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtr4i 3033 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1285    C_ wss 2974
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987
This theorem is referenced by: (None)
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