Theorem eqimss2 3053

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 3052	. 2 |- ( A = B -> A C_ B )
2	1	eqcoms 2085	1 |- ( B = A -> A C_ B )

Syntax hints:   -> wi 4   = wceq 1285   C_ wss 2974

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987

This theorem is referenced by:  disjeq2  3778  disjeq1  3781  poeq2  4063  seeq1  4102  seeq2  4103  dmcoeq  4632  xp11m  4789  funeq  4951  fconst3m  5412  tposeq  5896