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Theorem kmlem7 8557
 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 8556 . 2
2 ralinexa 2909 . . . . . 6
32rexbii 2959 . . . . 5
4 rexnal 2905 . . . . 5
53, 4bitri 249 . . . 4
65ralbii 2888 . . 3
7 ralnex 2903 . . 3
86, 7bitri 249 . 2
91, 8sylib 196 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  E.wrex 2808  i^icin 3474   c0 3784 This theorem is referenced by:  kmlem13  8563 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 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-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-nul 3785
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