Theorem sseqtr4i 3033

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 2086	. 2 |- B = C
4	1, 3	sseqtri 3032	1 |- A C_ C

Syntax hints:   = 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:  eqimss2i  3055  difdif2ss  3228  snsspr1  3541  snsspr2  3542  snsstp1  3543  snsstp2  3544  snsstp3  3545  prsstp12  3546  prsstp13  3547  prsstp23  3548  iunxdif2  3734  sssucid  4178  opabssxp  4440  dmresi  4691  cnvimass  4718  ssrnres  4793  cnvcnv  4803  cnvssrndm  4872  dmmpt2ssx  5856  tfrcllemssrecs  6001  sucinc  6089  ressxr  7224  ltrelxr  7240  nnssnn0  8358  un0addcl  8388  un0mulcl  8389  nn0ssxnn0  8421  fzossnn0  9261  isprm3  10644