Theorem eqimss2i 3258

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

Step	Hyp	Ref	Expression
1		ssid 3221	. 2 |- B C_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtrri 3236	1 |- B C_ A

Syntax hints:   = wceq 1373   C_ wss 3174

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-in 3180  df-ss 3187

This theorem is referenced by:  cocnvres  5226  cocnvss  5227  fsum3  11813  prodfclim1  11970  ef0lem  12086  restid  13197  hmeores  14902  struct2slots2dom  15752  struct2griedg  15760