Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  kmlem7 Structured version   Unicode version

Theorem kmlem7 8026
 Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 4 => 1. (Contributed by NM, 26-Mar-2004.)
Assertion
Ref Expression
kmlem7
Distinct variable group:   ,,,

Proof of Theorem kmlem7
StepHypRef Expression
1 kmlem6 8025 . 2
2 ralinexa 2742 . . . . . 6
32rexbii 2722 . . . . 5
4 rexnal 2708 . . . . 5
53, 4bitri 241 . . . 4
65ralbii 2721 . . 3
7 ralnex 2707 . . 3
86, 7bitri 241 . 2
91, 8sylib 189 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698   cin 3311  c0 3620 This theorem is referenced by:  kmlem13  8032 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-nul 3621
 Copyright terms: Public domain W3C validator