Theorem sseqtr4i 2978

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 2044	. 2 |- B = C
4	1, 3	sseqtri 2977	1 |- A C_ C

Syntax hints:   = wceq 1243   C_ wss 2917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931

This theorem is referenced by:  eqimss2i  3000  difdif2ss  3194  snsspr1  3512  snsspr2  3513  snsstp1  3514  snsstp2  3515  snsstp3  3516  prsstp12  3517  prsstp13  3518  prsstp23  3519  iunxdif2  3705  sssucid  4152  opabssxp  4414  dmresi  4661  cnvimass  4688  ssrnres  4763  cnvcnv  4773  cnvssrndm  4842  dmmpt2ssx  5825  sucinc  6025  ressxr  7069  ltrelxr  7080  nnssnn0  8184  un0addcl  8215  un0mulcl  8216  fzossnn0  9031