Theorem eqimss2i 3285

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 3248	. 2 |- B C_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtrri 3263	1 |- B C_ A

Syntax hints:   = wceq 1398   C_ wss 3201

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3207  df-ss 3214

This theorem is referenced by:  cocnvres  5268  cocnvss  5269  fsum3  12011  prodfclim1  12168  ef0lem  12284  restid  13396  hmeores  15109  struct2slots2dom  15962  struct2griedg  15970