Theorem eqimss2 3210

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 3209	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2180	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1353   C_ wss 3129

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142

This theorem is referenced by:  disjeq2  3984  disjeq1  3987  poeq2  4300  seeq1  4339  seeq2  4340  dmcoeq  4899  xp11m  5067  funeq  5236  fconst3m  5735  tposeq  6247  undifdcss  6921  ennnfonelemk  12395  ennnfonelemss  12405  qnnen  12426  imasaddfnlemg  12717  topgele  13420  topontopn  13428  txdis  13670