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Theorem prtlem14 26723
 Description: Lemma for prter1 26728, prter2 26730 and prtex 26729. (Contributed by Rodolfo Medina, 13-Oct-2010.)
Assertion
Ref Expression
prtlem14
Distinct variable groups:   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem prtlem14
StepHypRef Expression
1 df-prt 26721 . . 3
2 rsp2 2768 . . 3
31, 2sylbi 188 . 2
4 elin 3530 . . . 4
5 eq0 3642 . . . . . 6
6 sp 1763 . . . . . 6
75, 6sylbi 188 . . . . 5
87pm2.21d 100 . . . 4
94, 8syl5bir 210 . . 3
109prtlem1 26690 . 2
113, 10syl6 31 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 358   wa 359  wal 1549   wceq 1652   wcel 1725  wral 2705   cin 3319  c0 3628   wprt 26720 This theorem is referenced by:  prtlem15  26724  prtlem17  26725 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-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-ral 2710  df-v 2958  df-dif 3323  df-in 3327  df-nul 3629  df-prt 26721
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