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Theorem kmlem15 8612
 Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 5 <=> 4. (Contributed by NM, 4-Apr-2004.)
Hypotheses
Ref Expression
kmlem14.1
kmlem14.2
kmlem14.3
Assertion
Ref Expression
kmlem15
Distinct variable groups:   ,,,,   ,
Allowed substitution hints:   (,,,)   (,,,,)   (,,,,)

Proof of Theorem kmlem15
StepHypRef Expression
1 kmlem14.3 . . . 4
2 nfv 1769 . . . . . . 7
32eu1 2359 . . . . . 6
4 elin 3608 . . . . . . . . 9
5 clelsb3 2577 . . . . . . . . . . . 12
6 elin 3608 . . . . . . . . . . . 12
75, 6bitri 257 . . . . . . . . . . 11
8 equcom 1870 . . . . . . . . . . 11
97, 8imbi12i 333 . . . . . . . . . 10
109albii 1699 . . . . . . . . 9
114, 10anbi12i 711 . . . . . . . 8
12 19.28v 1833 . . . . . . . 8
1311, 12bitr4i 260 . . . . . . 7
1413exbii 1726 . . . . . 6
153, 14bitri 257 . . . . 5
1615ralbii 2823 . . . 4
17 df-ral 2761 . . . . 5
18 kmlem14.2 . . . . . . . . . 10
1918albii 1699 . . . . . . . . 9
20 19.21v 1794 . . . . . . . . 9
2119, 20bitri 257 . . . . . . . 8
2221exbii 1726 . . . . . . 7
23 19.37v 1834 . . . . . . 7
2422, 23bitri 257 . . . . . 6
2524albii 1699 . . . . 5
2617, 25bitr4i 260 . . . 4
271, 16, 263bitri 279 . . 3
2827anbi2i 708 . 2
29 19.28v 1833 . 2
30 19.28v 1833 . . . . 5
3130exbii 1726 . . . 4
32 19.42v 1842 . . . 4
3331, 32bitr2i 258 . . 3
3433albii 1699 . 2
3528, 29, 343bitr2i 281 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376  wal 1450  wex 1671  wsb 1805   wcel 1904  weu 2319   wne 2641  wral 2756   cin 3389 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-v 3033  df-in 3397 This theorem is referenced by:  kmlem16  8613
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