Theorem sseqtr4i 3032

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 2085	. 2 |- B = C
4	1, 3	sseqtri 3031	1 |- A C_ C

Syntax hints:   = wceq 1284   C_ wss 2973

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 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-in 2979  df-ss 2986

This theorem is referenced by:  eqimss2i  3054  difdif2ss  3221  snsspr1  3533  snsspr2  3534  snsstp1  3535  snsstp2  3536  snsstp3  3537  prsstp12  3538  prsstp13  3539  prsstp23  3540  iunxdif2  3726  sssucid  4170  opabssxp  4432  dmresi  4681  cnvimass  4708  ssrnres  4783  cnvcnv  4793  cnvssrndm  4862  dmmpt2ssx  5845  sucinc  6048  ressxr  7162  ltrelxr  7173  nnssnn0  8291  un0addcl  8321  un0mulcl  8322  fzossnn0  9184  isprm3  10500