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Theorem prtlem400 26720
 Description: Lemma for prter2 26731 and also a property of partitions . (Contributed by Rodolfo Medina, 15-Oct-2010.) (Revised by Mario Carneiro, 12-Aug-2015.)
Hypothesis
Ref Expression
prtlem13.1
Assertion
Ref Expression
prtlem400
Distinct variable group:   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem prtlem400
StepHypRef Expression
1 neirr 2607 . 2
2 prtlem13.1 . . . 4
32prtlem16 26719 . . 3
4 elqsn0 6974 . . 3
53, 4mpan 653 . 2
61, 5mto 170 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726   wne 2600  wrex 2707  c0 3629  cuni 4016  copab 4266   cdm 4879  cqs 6905 This theorem is referenced by:  prter2  26731 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 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 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 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-xp 4885  df-cnv 4887  df-dm 4889  df-rn 4890  df-res 4891  df-ima 4892  df-ec 6908  df-qs 6912
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