Theorem kmlem5 8555

Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 3 => 4. (Contributed by NM, 25-Mar-2004.)

Assertion

Ref	Expression
kmlem5

Distinct variable group:   ,,

Proof of Theorem kmlem5

Step	Hyp	Ref	Expression
1		difss 3630	. . . 4
2		sslin 3723	. . . 4
3	1, 2	ax-mp 5	. . 3
4		kmlem4 8554	. . 3
5	3, 4	syl5sseq 3551	. 2
6		ss0b 3815	. 2
7	5, 6	sylib 196	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  \cdif 3472  i^icin 3474  C_wss 3475  c0 3784  {csn 4029  U.cuni 4249

This theorem is referenced by:  kmlem9  8559

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-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-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-uni 4250