Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  trsucss Structured version   Unicode version

Theorem trsucss 4660
 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

Proof of Theorem trsucss
StepHypRef Expression
1 elsuci 4640 . 2
2 trss 4304 . . 3
3 eqimss 3393 . . . 4
43a1i 11 . . 3
52, 4jaod 370 . 2
61, 5syl5 30 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 358   wceq 1652   wcel 1725   wss 3313   wtr 4295   csuc 4576 This theorem is referenced by:  efgmnvl  15339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-v 2951  df-un 3318  df-in 3320  df-ss 3327  df-sn 3813  df-uni 4009  df-tr 4296  df-suc 4580
 Copyright terms: Public domain W3C validator