Theorem eqimss2 3157

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 3156	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2143	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1332   C_ wss 3076

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3082  df-ss 3089

This theorem is referenced by:  disjeq2  3918  disjeq1  3921  poeq2  4230  seeq1  4269  seeq2  4270  dmcoeq  4819  xp11m  4985  funeq  5151  fconst3m  5647  tposeq  6152  undifdcss  6819  ennnfonelemk  11949  ennnfonelemss  11959  qnnen  11980  topgele  12235  topontopn  12243  txdis  12485