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Theorem prnmax 8499
 Description: A positive real has no largest member. Definition 9-3.1(iii) of [Gleason] p. 121. (Contributed by NM, 9-Mar-1996.) (Revised by Mario Carneiro, 11-May-2013.) (New usage is discouraged.)
Assertion
Ref Expression
prnmax
Distinct variable groups:   ,   ,

Proof of Theorem prnmax
StepHypRef Expression
1 eleq1 2313 . . . . 5
21anbi2d 687 . . . 4
3 breq1 3923 . . . . 5
43rexbidv 2528 . . . 4
52, 4imbi12d 313 . . 3
6 elnpi 8492 . . . . . 6
76simprbi 452 . . . . 5
87r19.21bi 2603 . . . 4
98simprd 451 . . 3
105, 9vtoclg 2781 . 2
1110anabsi7 795 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   w3a 939  wal 1532   wceq 1619   wcel 1621  wral 2509  wrex 2510  cvv 2727   wpss 3079  c0 3362   class class class wbr 3920  cnq 8354   cltq 8360  cnp 8361 This theorem is referenced by:  npomex  8500  prnmadd  8501  genpnmax  8511  1idpr  8533  ltexprlem4  8543  reclem3pr  8553  suplem1pr  8556 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-pss 3091  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921  df-np 8485
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