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Theorem kmlem16 8001
 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 7999 . . 3
51, 2, 3kmlem15 8000 . . . 4
65exbii 1589 . . 3
74, 6orbi12i 508 . 2
8 19.43 1612 . 2
9 pm3.24 853 . . . . . 6
10 simpl 444 . . . . . . . . 9
1110sps 1766 . . . . . . . 8
1211exlimivv 1642 . . . . . . 7
13 simpl 444 . . . . . . . . 9
1413sps 1766 . . . . . . . 8
1514exlimivv 1642 . . . . . . 7
1612, 15anim12i 550 . . . . . 6
179, 16mto 169 . . . . 5
18 19.33b 1615 . . . . 5
1917, 18ax-mp 8 . . . 4
2010exlimiv 1641 . . . . . . . . . 10
2113exlimiv 1641 . . . . . . . . . 10
2220, 21anim12i 550 . . . . . . . . 9
239, 22mto 169 . . . . . . . 8
24 19.33b 1615 . . . . . . . 8
2523, 24ax-mp 8 . . . . . . 7
2625exbii 1589 . . . . . 6
27 19.43 1612 . . . . . 6
2826, 27bitr2i 242 . . . . 5
2928albii 1572 . . . 4
3019, 29bitr3i 243 . . 3
3130exbii 1589 . 2
327, 8, 313bitr2i 265 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359  wal 1546  wex 1547   wcel 1721  weu 2254   wne 2567  wral 2666  wrex 2667   cin 3279 This theorem is referenced by:  dfackm  8002 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-v 2918  df-in 3287
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