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

Theorem trsucss 4126
Description: A member of the successor of a transitive class is a subclass of it. (Contributed by NM, 4-Oct-2003.)
Assertion
Ref Expression
trsucss  Tr  suc 
C_

Proof of Theorem trsucss
StepHypRef Expression
1 elsuci 4106 . 2  suc
2 trss 3854 . . 3  Tr  C_
3 eqimss 2991 . . . 4  C_
43a1i 9 . . 3  Tr  C_
52, 4jaod 636 . 2  Tr  C_
61, 5syl5 28 1  Tr  suc 
C_
Colors of variables: wff set class
Syntax hints:   wi 4   wo 628   wceq 1242   wcel 1390    C_ wss 2911   Tr wtr 3845   suc csuc 4068
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  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-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-uni 3572  df-tr 3846  df-suc 4074
This theorem is referenced by:  onsucsssucr  4200  ordpwsucss  4243
  Copyright terms: Public domain W3C validator