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Theorem prtlem13 26731
 Description: Lemma for prter1 26742, prter2 26744, prter3 26745 and prtex 26743. (Contributed by Rodolfo Medina, 13-Oct-2010.) (Revised by Mario Carneiro, 12-Aug-2015.)
Hypothesis
Ref Expression
prtlem13.1
Assertion
Ref Expression
prtlem13
Distinct variable groups:   ,,,,   ,,,   ,,,
Allowed substitution hints:   (,)   (,,,,,)

Proof of Theorem prtlem13
StepHypRef Expression
1 vex 2961 . 2
2 vex 2961 . 2
3 elequ2 1731 . . . . 5
4 elequ2 1731 . . . . 5
53, 4anbi12d 693 . . . 4
65cbvrexv 2935 . . 3
7 eleq1 2498 . . . . 5
8 eleq1 2498 . . . . 5
97, 8bi2anan9 845 . . . 4
109rexbidv 2728 . . 3
116, 10syl5bb 250 . 2
12 prtlem13.1 . 2
131, 2, 11, 12braba 4475 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653  wrex 2708   class class class wbr 4215  copab 4268 This theorem is referenced by:  prtlem16  26732  prtlem18  26740  prter1  26742  prter3  26745 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 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270
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