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Theorem prtlem15 26726
 Description: Lemma for prter1 26730 and prtex 26731. (Contributed by Rodolfo Medina, 13-Oct-2010.)
Assertion
Ref Expression
prtlem15
Distinct variable groups:   ,,,,,   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem prtlem15
StepHypRef Expression
1 anabs7 787 . . . . . . 7
2 an43 26697 . . . . . . . 8
32anbi2i 677 . . . . . . 7
41, 3, 23bitr4ri 271 . . . . . 6
5 prtlem14 26725 . . . . . . . 8
6 an3 26699 . . . . . . . . 9
7 elequ2 1731 . . . . . . . . . 10
87anbi2d 686 . . . . . . . . 9
96, 8syl5ibr 214 . . . . . . . 8
105, 9syl8 68 . . . . . . 7
1110imp4a 574 . . . . . 6
124, 11syl7bi 223 . . . . 5
1312expdimp 428 . . . 4
1413rexlimdv 2831 . . 3
1514reximdva 2820 . 2
16 elequ2 1731 . . . 4
17 elequ2 1731 . . . 4
1816, 17anbi12d 693 . . 3
1918cbvrexv 2935 . 2
2015, 19syl6ib 219 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726  wrex 2708   wprt 26722 This theorem is referenced by:  prter1  26730 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-in 3329  df-nul 3631  df-prt 26723
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