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

Step	Hyp	Ref	Expression
1		vprc 4590	. . 3
2	1	nelir 2793	. 2
3		ruv 8048	. . 3
4		neleq1 2795	. . 3
5	3, 4	ax-mp 5	. 2
6	2, 5	mpbir 209	1

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