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Theorem sseqtr4i 2972
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995.)
Hypotheses
Ref Expression
sseqtr4.1 AB
sseqtr4.2 𝐶 = B
Assertion
Ref Expression
sseqtr4i A𝐶

Proof of Theorem sseqtr4i
StepHypRef Expression
1 sseqtr4.1 . 2 AB
2 sseqtr4.2 . . 3 𝐶 = B
32eqcomi 2041 . 2 B = 𝐶
41, 3sseqtri 2971 1 A𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1242  wss 2911
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  eqimss2i  2994  difdif2ss  3188  snsspr1  3503  snsspr2  3504  snsstp1  3505  snsstp2  3506  snsstp3  3507  prsstp12  3508  prsstp13  3509  prsstp23  3510  iunxdif2  3696  sssucid  4118  opabssxp  4357  dmresi  4604  cnvimass  4631  ssrnres  4706  cnvcnv  4716  cnvssrndm  4785  dmmpt2ssx  5767  sucinc  5964  ressxr  6846  ltrelxr  6857  nnssnn0  7940  un0addcl  7971  un0mulcl  7972  fzossnn0  8781
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