Theorem eqimss2 3248

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 3247	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2208	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1373   C_ wss 3166

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179

This theorem is referenced by:  disjeq2  4025  disjeq1  4028  poeq2  4348  seeq1  4387  seeq2  4388  dmcoeq  4952  xp11m  5122  funeq  5292  fconst3m  5805  tposeq  6335  undifdcss  7022  nninfctlemfo  12394  ennnfonelemk  12804  ennnfonelemss  12814  qnnen  12835  imasaddfnlemg  13179  topgele  14534  topontopn  14542  txdis  14782  edgstruct  15691