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Theorem kmlem6 8027
 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:   ,   ,,   ,,,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem kmlem6
StepHypRef Expression
1 r19.26 2830 . 2
2 n0 3629 . . . . 5
32biimpi 187 . . . 4
4 ne0i 3626 . . . . . . . 8
54necon2bi 2644 . . . . . . 7
65imim2i 14 . . . . . 6
76ralimi 2773 . . . . 5
87alrimiv 1641 . . . 4
9 19.29r 1607 . . . . 5
10 df-rex 2703 . . . . 5
119, 10sylibr 204 . . . 4
123, 8, 11syl2an 464 . . 3
1312ralimi 2773 . 2
141, 13sylbir 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  c0 3620 This theorem is referenced by:  kmlem7  8028 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-nul 3621
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