Theorem eqimss2i 3305

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 3268	. 2 |- B C_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtrri 3283	1 |- B C_ A

Syntax hints:   = wceq 1402   C_ wss 3220

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233

This theorem is referenced by:  cocnvres  5307  cocnvss  5308  fsum3  12132  prodfclim1  12289  ef0lem  12405  restid  13581  hmeores  15339  struct2slots2dom  16193  struct2griedg  16201