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Theorem ltprord 9429
Description: Positive real 'less than' in terms of proper subset. (Contributed by NM, 20-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
ltprord

Proof of Theorem ltprord
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq1 2529 . . . . 5
21anbi1d 704 . . . 4
3 psseq1 3590 . . . 4
42, 3anbi12d 710 . . 3
5 eleq1 2529 . . . . 5
65anbi2d 703 . . . 4
7 psseq2 3591 . . . 4
86, 7anbi12d 710 . . 3
9 df-ltp 9384 . . 3
104, 8, 9brabg 4771 . 2
1110bianabs 880 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  C.wpss 3476   class class class wbr 4452   cnp 9258   cltp 9262
This theorem is referenced by:  ltsopr  9431  ltaddpr  9433  ltexprlem7  9441  ltexpri  9442  suplem1pr  9451  suplem2pr  9452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-ltp 9384
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