Theorem sseqtrri 3259

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995.)

Hypotheses

Ref	Expression
sseqtrri.1	|- A C_ B
sseqtrri.2	|- C = B

Assertion

Ref	Expression
sseqtrri	|- A C_ C

Proof of Theorem sseqtrri

Step	Hyp	Ref	Expression
1		sseqtrri.1	. 2 |- A C_ B
2		sseqtrri.2	. . 3 |- C = B
3	2	eqcomi 2233	. 2 |- B = C
4	1, 3	sseqtri 3258	1 |- A C_ C

Syntax hints:   = wceq 1395   C_ wss 3197

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210

This theorem is referenced by:  eqimss2i  3281  difdif2ss  3461  snsspr1  3815  snsspr2  3816  snsstp1  3817  snsstp2  3818  snsstp3  3819  prsstp12  3820  prsstp13  3821  prsstp23  3822  iunxdif2  4013  pwpwssunieq  4053  sssucid  4505  opabssxp  4792  dmresi  5059  cnvimass  5090  ssrnres  5170  cnvcnv  5180  cnvssrndm  5249  dmmpossx  6343  tfrcllemssrecs  6496  sucinc  6589  mapex  6799  exmidpw  7066  exmidpweq  7067  casefun  7248  djufun  7267  pw1ne1  7410  ressxr  8186  ltrelxr  8203  nnssnn0  9368  un0addcl  9398  un0mulcl  9399  nn0ssxnn0  9431  fzssnn  10260  fzossnn0  10369  isumclim3  11929  isprm3  12635  phimullem  12742  tgvalex  13291  eqgfval  13754  cnfldbas  14518  mpocnfldadd  14519  mpocnfldmul  14521  cnfldcj  14523  cnfldtset  14524  cnfldle  14525  cnfldds  14526  cnrest2  14904  qtopbasss  15189  tgqioo  15223