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Theorem ltprord 8912
 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 2498 . . . . 5
21anbi1d 687 . . . 4
3 psseq1 3436 . . . 4
42, 3anbi12d 693 . . 3
5 eleq1 2498 . . . . 5
65anbi2d 686 . . . 4
7 psseq2 3437 . . . 4
86, 7anbi12d 693 . . 3
9 df-ltp 8867 . . 3
104, 8, 9brabg 4477 . 2
1110bianabs 852 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726   wpss 3323   class class class wbr 4215  cnp 8739   cltp 8743 This theorem is referenced by:  ltsopr  8914  ltaddpr  8916  ltexprlem7  8924  ltexpri  8925  suplem1pr  8934  suplem2pr  8935 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-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-ltp 8867
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