Theorem eqimssi 3235

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 3199	. 2 |- A C_ A
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtri 3213	1 |- A C_ B

Syntax hints:   = wceq 1364   C_ wss 3153

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3159  df-ss 3166

This theorem is referenced by:  funi  5286  fpr  5740  elfzo1  10257  sumsplitdc  11575  isumlessdc  11639  nconstwlpolem0  15553