Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sucidVD Structured version   Unicode version

Theorem sucidVD 37130
Description: A set belongs to its successor. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sucid 5518 is sucidVD 37130 without virtual deductions and was automatically derived from sucidVD 37130.
 h1:: 2:1: 3:2: 4:: qed:3,4:
(Contributed by Alan Sare, 18-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
sucidVD.1
Assertion
Ref Expression
sucidVD

Proof of Theorem sucidVD
StepHypRef Expression
1 sucidVD.1 . . . 4
21snid 4024 . . 3
3 elun2 3634 . . 3
42, 3e0a 37020 . 2
5 df-suc 5445 . 2
64, 5eleqtrri 2509 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1868  cvv 3081   cun 3434  csn 3996   csuc 5441 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-un 3441  df-in 3443  df-ss 3450  df-sn 3997  df-suc 5445 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator