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Theorem en3lplem2 8053
Description: Lemma for en3lp 8054. (Contributed by Alan Sare, 28-Oct-2011.)
Assertion
Ref Expression
en3lplem2
Distinct variable groups:   ,   ,   ,

Proof of Theorem en3lplem2
StepHypRef Expression
1 en3lplem1 8052 . . . . 5
2 en3lplem1 8052 . . . . . . . 8
323comr 1204 . . . . . . 7
43a1d 25 . . . . . 6
5 tprot 4125 . . . . . . . . 9
65ineq2i 3696 . . . . . . . 8
76neeq1i 2742 . . . . . . 7
87bicomi 202 . . . . . 6
94, 8syl8ib 231 . . . . 5
10 jao 512 . . . . 5
111, 9, 10sylsyld 56 . . . 4
1211imp 429 . . 3
13 en3lplem1 8052 . . . . . . 7
14133coml 1203 . . . . . 6
1514a1d 25 . . . . 5
16 tprot 4125 . . . . . . 7
1716ineq2i 3696 . . . . . 6
1817neeq1i 2742 . . . . 5
1915, 18syl8ib 231 . . . 4
2019imp 429 . . 3
21 idd 24 . . . . . . 7
22 dftp2 4075 . . . . . . . 8
2322eleq2i 2535 . . . . . . 7
2421, 23syl6ib 226 . . . . . 6
25 abid 2444 . . . . . 6
2624, 25syl6ib 226 . . . . 5
27 df-3or 974 . . . . 5
2826, 27syl6ib 226 . . . 4
2928imp 429 . . 3
3012, 20, 29mpjaod 381 . 2
3130ex 434 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  /\wa 369  \/w3o 972  /\w3a 973  =wceq 1395  e.wcel 1818  {cab 2442  =/=wne 2652  i^icin 3474   c0 3784  {ctp 4033
This theorem is referenced by:  en3lp  8054
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
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  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-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-nul 3785  df-sn 4030  df-pr 4032  df-tp 4034
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