ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sseqtr4i Structured version   GIF version

Theorem sseqtr4i 2951
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 2022 . 2 B = 𝐶
41, 3sseqtri 2950 1 A𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1226  wss 2890
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-11 1374  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-in 2897  df-ss 2904
This theorem is referenced by:  eqimss2i  2973  difdif2ss  3167  snsspr1  3482  snsspr2  3483  snsstp1  3484  snsstp2  3485  snsstp3  3486  prsstp12  3487  prsstp13  3488  prsstp23  3489  iunxdif2  3675  sssucid  4097  opabssxp  4337  dmresi  4584  cnvimass  4611  ssrnres  4686  cnvcnv  4696  cnvssrndm  4765  dmmpt2ssx  5744  tfrlemi14  5865  sucinc  5936  ressxr  6671  ltrelxr  6682
  Copyright terms: Public domain W3C validator