Theorem eqimss2 3082

Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.)

Assertion

Ref	Expression
eqimss2	|- ( B = A -> A C_ B )

Proof of Theorem eqimss2

Step	Hyp	Ref	Expression
1		eqimss 3081	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2092	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1290   C_ wss 3002

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3008  df-ss 3015

This theorem is referenced by:  disjeq2  3834  disjeq1  3837  poeq2  4138  seeq1  4177  seeq2  4178  dmcoeq  4720  xp11m  4884  funeq  5050  fconst3m  5532  tposeq  6028  undifdcss  6689  topgele  11790  topontopn  11798