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

Theorem sseqtr4i 3006
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 2060 . 2 𝐵 = 𝐶
41, 3sseqtri 3005 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  eqimss2i  3028  difdif2ss  3222  snsspr1  3540  snsspr2  3541  snsstp1  3542  snsstp2  3543  snsstp3  3544  prsstp12  3545  prsstp13  3546  prsstp23  3547  iunxdif2  3733  sssucid  4180  opabssxp  4442  dmresi  4689  cnvimass  4716  ssrnres  4791  cnvcnv  4801  cnvssrndm  4870  dmmpt2ssx  5853  sucinc  6056  ressxr  7128  ltrelxr  7139  nnssnn0  8242  un0addcl  8272  un0mulcl  8273  fzossnn0  9133
  Copyright terms: Public domain W3C validator