Theorem eqimssi 3080

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 3044	. 2 |- A C_ A
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtri 3058	1 |- A C_ B

Syntax hints:   = wceq 1289   C_ wss 2999

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012

This theorem is referenced by:  funi  5046  fpr  5479  elfzo1  9601  sumsplitdc  10826  isumlessdc  10890