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Theorem kmlem1 8551
Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, 1 => 2. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
kmlem1
Distinct variable groups:   , ,   ,   , , ,

Proof of Theorem kmlem1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 3112 . . . . . 6
21rabex 4603 . . . . 5
3 raleq 3054 . . . . . . 7
4 raleq 3054 . . . . . . . 8
54raleqbi1dv 3062 . . . . . . 7
63, 5anbi12d 710 . . . . . 6
7 raleq 3054 . . . . . . 7
87exbidv 1714 . . . . . 6
96, 8imbi12d 320 . . . . 5
102, 9spcv 3200 . . . 4
1110alrimiv 1719 . . 3
12 elrabi 3254 . . . . . . . 8
13 elrabi 3254 . . . . . . . . . 10
1413imim1i 58 . . . . . . . . 9
1514ralimi2 2847 . . . . . . . 8
1612, 15imim12i 57 . . . . . . 7
1716ralimi2 2847 . . . . . 6
18 neeq1 2738 . . . . . . . . 9
1918elrab 3257 . . . . . . . 8
2019simprbi 464 . . . . . . 7
2120rgen 2817 . . . . . 6
2217, 21jctil 537 . . . . 5
2319biimpri 206 . . . . . . . . 9
2423imim1i 58 . . . . . . . 8
2524expd 436 . . . . . . 7
2625ralimi2 2847 . . . . . 6
2726eximi 1656 . . . . 5
2822, 27imim12i 57 . . . 4
2928alimi 1633 . . 3
3011, 29syl 16 . 2
31 raleq 3054 . . . . 5
3231raleqbi1dv 3062 . . . 4
33 raleq 3054 . . . . 5
3433exbidv 1714 . . . 4
3532, 34imbi12d 320 . . 3
3635cbvalv 2023 . 2
3730, 36sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652  A.wral 2807  {crab 2811   c0 3784
This theorem is referenced by:  kmlem13  8563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489
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