Theorem eqimss2 3183

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 3182	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2160	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1335   C_ wss 3102

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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115

This theorem is referenced by:  disjeq2  3947  disjeq1  3950  poeq2  4261  seeq1  4300  seeq2  4301  dmcoeq  4859  xp11m  5025  funeq  5191  fconst3m  5687  tposeq  6195  undifdcss  6868  ennnfonelemk  12171  ennnfonelemss  12181  qnnen  12202  topgele  12469  topontopn  12477  txdis  12719