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

Theorem ruALT 7569
 Description: Alternate proof of Russell's Paradox ru 3160, simplified using (indirectly) the Axiom of Regularity ax-reg 7560. (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 4341 . . 3
2 df-nel 2602 . . 3
31, 2mpbir 201 . 2
4 ruv 7568 . . 3
5 neleq1 2699 . . 3
64, 5ax-mp 8 . 2
73, 6mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wceq 1652   wcel 1725  cab 2422   wnel 2600  cvv 2956 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-reg 7560 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-ne 2601  df-nel 2602  df-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821
 Copyright terms: Public domain W3C validator