Theorem eqimss2i 3250

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 3213	. 2 |- B C_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtrri 3228	1 |- B C_ A

Syntax hints:   = wceq 1373   C_ wss 3166

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179

This theorem is referenced by:  cocnvres  5207  cocnvss  5208  fsum3  11698  prodfclim1  11855  ef0lem  11971  restid  13082  hmeores  14787  struct2slots2dom  15635  struct2griedg  15643