Theorem sseq1i 3039

Description: An equality inference for the subclass relationship. (Contributed by NM, 18-Aug-1993.)

Hypothesis

Ref	Expression
sseq1i.1	|- A = B

Assertion

Ref	Expression
sseq1i	|- ( A C_ C <-> B C_ C )

Proof of Theorem sseq1i

Step	Hyp	Ref	Expression
1		sseq1i.1	. 2 |- A = B
2		sseq1 3036	. 2 |- ( A = B -> ( A C_ C <-> B C_ C ) )
3	1, 2	ax-mp 7	1 |- ( A C_ C <-> B C_ C )

Syntax hints:   <-> wb 103   = wceq 1287   C_ wss 2988

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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-in 2994  df-ss 3001

This theorem is referenced by:  eqsstri  3045  syl5eqss  3059  ssab  3080  rabss  3087  uniiunlem  3098  prss  3576  prssg  3577  tpss  3585  iunss  3754  pwtr  4020  ordsucss  4294  elnn  4393  cores2  4909  dffun2  4991  funimaexglem  5062  idref  5497  ordgt0ge1  6153  prarloclemn  7002  bdeqsuc  11210  bj-omssind  11268