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Theorem prtlem17 26763
 Description: Lemma for prter2 26768. (Contributed by Rodolfo Medina, 15-Oct-2010.)
Assertion
Ref Expression
prtlem17
Distinct variable groups:   ,,   ,,   ,
Allowed substitution hints:   (,)

Proof of Theorem prtlem17
StepHypRef Expression
1 df-rex 2717 . . 3
2 an32 775 . . . . . . . 8
3 prtlem14 26761 . . . . . . . . . . 11
4 elequ2 1732 . . . . . . . . . . . 12
54biimprd 216 . . . . . . . . . . 11
63, 5syl8 68 . . . . . . . . . 10
76exp4a 591 . . . . . . . . 9
87imp3a 422 . . . . . . . 8
92, 8syl5bir 211 . . . . . . 7
109exp3a 427 . . . . . 6
1110imp5a 583 . . . . 5
1211imp4b 575 . . . 4
1312exlimdv 1647 . . 3
141, 13syl5bi 210 . 2
1514ex 425 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wex 1551   wcel 1727  wrex 2712   wprt 26758 This theorem is referenced by:  prtlem18  26764 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-v 2964  df-dif 3309  df-in 3313  df-nul 3614  df-prt 26759
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