Theorem kmlem6 8556

Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 4 => 1. (Contributed by NM, 26-Mar-2004.)

Assertion

Ref	Expression
kmlem6

Distinct variable groups:   ,   ,,   ,,,

Proof of Theorem kmlem6

Step	Hyp	Ref	Expression
1		r19.26 2984	. 2
2		n0 3794	. . . . 5
3	2	biimpi 194	. . . 4
4		ne0i 3790	. . . . . . . 8
5	4	necon2bi 2694	. . . . . . 7
6	5	imim2i 14	. . . . . 6
7	6	ralimi 2850	. . . . 5
8	7	alrimiv 1719	. . . 4
9		19.29r 1684	. . . . 5
10		df-rex 2813	. . . . 5
11	9, 10	sylibr 212	. . . 4
12	3, 8, 11	syl2an 477	. . 3
13	12	ralimi 2850	. 2
14	1, 13	sylbir 213	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652  A.wral 2807  E.wrex 2808  c0 3784

This theorem is referenced by:  kmlem7  8557

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