Theorem eqimss2 3303

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 3302	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2241	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1402   C_ wss 3220

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233

This theorem is referenced by:  ifpprsnssdc  3815  disjeq2  4105  disjeq1  4108  poeq2  4440  seeq1  4479  seeq2  4480  dmcoeq  5050  xp11m  5221  funeq  5392  fconst3m  5925  tposeq  6508  mapssfsetg  6936  undifdcss  7220  nninfctlemfo  12795  ennnfonelemk  13269  ennnfonelemss  13279  qnnen  13300  imasaddfnlemg  13612  topgele  15053  topontopn  15061  txdis  15301  edgstruct  16219