Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sess2 Unicode version

Theorem sess2 4853
 Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.)
Assertion
Ref Expression
sess2

Proof of Theorem sess2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssralv 3563 . . 3
2 rabss2 3582 . . . . 5
3 ssexg 4598 . . . . . 6
43ex 434 . . . . 5
52, 4syl 16 . . . 4
65ralimdv 2867 . . 3
71, 6syld 44 . 2
8 df-se 4844 . 2
9 df-se 4844 . 2
107, 8, 93imtr4g 270 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  {crab 2811   cvv 3109  C_wss 3475   class class class wbr 4452  Sewse 4841 This theorem is referenced by:  seeq2  4857  wereu2  4881  frmin  29322  wfrlem5  29347  frrlem5  29391 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-se 4844
 Copyright terms: Public domain W3C validator