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Theorem ruALT 8049
 Description: Alternate proof of ru 3326, simplified using (indirectly) the Axiom of Regularity ax-reg 8039. (Contributed by Alan Sare, 4-Oct-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ruALT

Proof of Theorem ruALT
StepHypRef Expression
1 vprc 4590 . . 3
21nelir 2793 . 2
3 ruv 8048 . . 3
4 neleq1 2795 . . 3
53, 4ax-mp 5 . 2
62, 5mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  {cab 2442  e/wnel 2653   cvv 3109 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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-reg 8039 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-ne 2654  df-nel 2655  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032
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