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Theorem kmlem16 8050
 Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4 5 <=> 4. (Contributed by NM, 4-Apr-2004.)
Hypotheses
Ref Expression
kmlem14.1
kmlem14.2
kmlem14.3
Assertion
Ref Expression
kmlem16
Distinct variable groups:   ,,,,,   ,
Allowed substitution hints:   (,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem kmlem16
StepHypRef Expression
1 kmlem14.1 . . . 4
2 kmlem14.2 . . . 4
3 kmlem14.3 . . . 4
41, 2, 3kmlem14 8048 . . 3
51, 2, 3kmlem15 8049 . . . 4
65exbii 1593 . . 3
74, 6orbi12i 509 . 2
8 19.43 1616 . 2
9 pm3.24 854 . . . . . 6
10 simpl 445 . . . . . . . . 9
1110sps 1771 . . . . . . . 8
1211exlimivv 1646 . . . . . . 7
13 simpl 445 . . . . . . . . 9
1413sps 1771 . . . . . . . 8
1514exlimivv 1646 . . . . . . 7
1612, 15anim12i 551 . . . . . 6
179, 16mto 170 . . . . 5
18 19.33b 1619 . . . . 5
1917, 18ax-mp 5 . . . 4
2010exlimiv 1645 . . . . . . . . . 10
2113exlimiv 1645 . . . . . . . . . 10
2220, 21anim12i 551 . . . . . . . . 9
239, 22mto 170 . . . . . . . 8
24 19.33b 1619 . . . . . . . 8
2523, 24ax-mp 5 . . . . . . 7
2625exbii 1593 . . . . . 6
27 19.43 1616 . . . . . 6
2826, 27bitr2i 243 . . . . 5
2928albii 1576 . . . 4
3019, 29bitr3i 244 . . 3
3130exbii 1593 . 2
327, 8, 313bitr2i 266 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wo 359   wa 360  wal 1550  wex 1551   wcel 1726  weu 2283   wne 2601  wral 2707  wrex 2708   cin 3321 This theorem is referenced by:  dfackm  8051 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-in 3329
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