Theorem eqimssi 3294

Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)

Hypothesis

Ref	Expression
eqimssi.1	|- A = B

Assertion

Ref	Expression
eqimssi	|- A C_ B

Proof of Theorem eqimssi

Step	Hyp	Ref	Expression
1		ssid 3258	. 2 |- A C_ A
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtri 3272	1 |- A C_ B

Syntax hints:   = wceq 1398   C_ wss 3211

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 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224

This theorem is referenced by:  funi  5384  fpr  5866  elfzo1  10530  sumsplitdc  12118  isumlessdc  12182  nconstwlpolem0  16849