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Theorem prnmax 8832
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2468 . . . . 5
21anbi2d 685 . . . 4
3 breq1 4179 . . . . 5
43rexbidv 2691 . . . 4
52, 4imbi12d 312 . . 3
6 elnpi 8825 . . . . . 6
76simprbi 451 . . . . 5
87r19.21bi 2768 . . . 4
98simprd 450 . . 3
105, 9vtoclg 2975 . 2
1110anabsi7 793 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936  wal 1546   wceq 1649   wcel 1721  wral 2670  wrex 2671  cvv 2920   wpss 3285  c0 3592   class class class wbr 4176  cnq 8687   cltq 8693  cnp 8694 This theorem is referenced by:  npomex  8833  prnmadd  8834  genpnmax  8844  1idpr  8866  ltexprlem4  8876  reclem3pr  8886  suplem1pr  8889 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-pss 3300  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-br 4177  df-np 8818
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