Theorem sseqtr4i 3059

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

Hypotheses

Ref	Expression
sseqtr4.1	|- A C_ B
sseqtr4.2	|- C = B

Assertion

Ref	Expression
sseqtr4i	|- A C_ C

Proof of Theorem sseqtr4i

Step	Hyp	Ref	Expression
1		sseqtr4.1	. 2 |- A C_ B
2		sseqtr4.2	. . 3 |- C = B
3	2	eqcomi 2092	. 2 |- B = C
4	1, 3	sseqtri 3058	1 |- A C_ C

Syntax hints:   = wceq 1289   C_ wss 2999

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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012

This theorem is referenced by:  eqimss2i  3081  difdif2ss  3256  snsspr1  3585  snsspr2  3586  snsstp1  3587  snsstp2  3588  snsstp3  3589  prsstp12  3590  prsstp13  3591  prsstp23  3592  iunxdif2  3778  pwpwssunieq  3817  sssucid  4242  opabssxp  4512  dmresi  4767  cnvimass  4795  ssrnres  4873  cnvcnv  4883  cnvssrndm  4952  dmmpt2ssx  5969  tfrcllemssrecs  6117  sucinc  6206  mapex  6409  exmidpw  6622  casefun  6774  djufun  6782  ressxr  7529  ltrelxr  7545  nnssnn0  8674  un0addcl  8704  un0mulcl  8705  nn0ssxnn0  8737  fzossnn0  9582  isumclim3  10813  isprm3  11374  phimullem  11475