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

Step	Hyp	Ref	Expression
1		kmlem6 8556	. 2
2		ralinexa 2909	. . . . . 6
3	2	rexbii 2959	. . . . 5
4		rexnal 2905	. . . . 5
5	3, 4	bitri 249	. . . 4
6	5	ralbii 2888	. . 3
7		ralnex 2903	. . 3
8	6, 7	bitri 249	. 2
9	1, 8	sylib 196	1

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