Theorem eqimss2i 2115

Description: Infer subclass relationship from equality.

Hypothesis

Ref	Expression
eqimssi.1	|- A = B

Assertion

Ref	Expression
eqimss2i	|- B (_ A

Proof of Theorem eqimss2i

Step	Hyp	Ref	Expression
1		ssid 2083	. 2 |- B (_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtr4 2097	1 |- B (_ A

Syntax hints:   = wceq 958   (_ wss 2050

This theorem is referenced by:  cvganz 6924  cvganuz 6925  clmnns 7084  climfnn 7092  2climnn 7102  2climnn0 7103  climaddlem3 7116  climubi 7153  climcau 7156  reccnv 7218  expcnv 7233  lmbr2 7926  minveclem15 8555  h2hlm 8845  occllem6 9173  projlem25 9205  projlem26 9206

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-in 2054  df-ss 2056

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