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Theorem en3lplem2 7671
 Description: Lemma for en3lp 7672. (Contributed by Alan Sare, 28-Oct-2011.)
Assertion
Ref Expression
en3lplem2
Distinct variable groups:   ,   ,   ,

Proof of Theorem en3lplem2
StepHypRef Expression
1 en3lplem1 7670 . . . . 5
2 en3lplem1 7670 . . . . . . . 8
323comr 1161 . . . . . . 7
43a1d 23 . . . . . 6
5 tprot 3899 . . . . . . . . 9
65ineq2i 3539 . . . . . . . 8
76neeq1i 2611 . . . . . . 7
87bicomi 194 . . . . . 6
94, 8syl8ib 223 . . . . 5
10 jao 499 . . . . 5
111, 9, 10sylsyld 54 . . . 4
1211imp 419 . . 3
13 en3lplem1 7670 . . . . . . 7
14133coml 1160 . . . . . 6
1514a1d 23 . . . . 5
16 tprot 3899 . . . . . . 7
1716ineq2i 3539 . . . . . 6
1817neeq1i 2611 . . . . 5
1915, 18syl8ib 223 . . . 4
2019imp 419 . . 3
21 idd 22 . . . . . . 7
22 dftp2 3854 . . . . . . . 8
2322eleq2i 2500 . . . . . . 7
2421, 23syl6ib 218 . . . . . 6
25 abid 2424 . . . . . 6
2624, 25syl6ib 218 . . . . 5
27 df-3or 937 . . . . 5
2826, 27syl6ib 218 . . . 4
2928imp 419 . . 3
3012, 20, 29mpjaod 371 . 2
3130ex 424 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 358   wa 359   w3o 935   w3a 936   wceq 1652   wcel 1725  cab 2422   wne 2599   cin 3319  c0 3628  ctp 3816 This theorem is referenced by:  en3lp  7672 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-nul 3629  df-sn 3820  df-pr 3821  df-tp 3822
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