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Theorem kmlem15 8046
 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 1630 . . . . . . 7
32eu1 2304 . . . . . 6
4 elin 3532 . . . . . . . . 9
5 clelsb3 2540 . . . . . . . . . . . 12
6 elin 3532 . . . . . . . . . . . 12
75, 6bitri 242 . . . . . . . . . . 11
8 equcom 1693 . . . . . . . . . . 11
97, 8imbi12i 318 . . . . . . . . . 10
109albii 1576 . . . . . . . . 9
114, 10anbi12i 680 . . . . . . . 8
12 19.28v 1919 . . . . . . . 8
1311, 12bitr4i 245 . . . . . . 7
1413exbii 1593 . . . . . 6
153, 14bitri 242 . . . . 5
1615ralbii 2731 . . . 4
17 df-ral 2712 . . . . 5
18 kmlem14.2 . . . . . . . . . 10
1918albii 1576 . . . . . . . . 9
20 19.21v 1914 . . . . . . . . 9
2119, 20bitri 242 . . . . . . . 8
2221exbii 1593 . . . . . . 7
23 19.37v 1923 . . . . . . 7
2422, 23bitri 242 . . . . . 6
2524albii 1576 . . . . 5
2617, 25bitr4i 245 . . . 4
271, 16, 263bitri 264 . . 3
2827anbi2i 677 . 2
29 19.28v 1919 . 2
30 19.28v 1919 . . . . 5
3130exbii 1593 . . . 4
32 19.42v 1929 . . . 4
3331, 32bitr2i 243 . . 3
3433albii 1576 . 2
3528, 29, 343bitr2i 266 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wex 1551  wsb 1659   wcel 1726  weu 2283   wne 2601  wral 2707   cin 3321 This theorem is referenced by:  kmlem16  8047 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-in 3329
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