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Theorem kmlem5 8034
 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
StepHypRef Expression
1 difss 3474 . . . 4
2 sslin 3567 . . . 4
31, 2ax-mp 8 . . 3
4 kmlem4 8033 . . 3
53, 4syl5sseq 3396 . 2
6 ss0b 3657 . 2
75, 6sylib 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wne 2599   cdif 3317   cin 3319   wss 3320  c0 3628  csn 3814  cuni 4015 This theorem is referenced by:  kmlem9  8038 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-uni 4016
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