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Theorem ltprord 9420
 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 2539 . . . . 5
21anbi1d 704 . . . 4
3 psseq1 3596 . . . 4
42, 3anbi12d 710 . . 3
5 eleq1 2539 . . . . 5
65anbi2d 703 . . . 4
7 psseq2 3597 . . . 4
86, 7anbi12d 710 . . 3
9 df-ltp 9375 . . 3
104, 8, 9brabg 4772 . 2
1110bianabs 878 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379   wcel 1767   wpss 3482   class class class wbr 4453  cnp 9249   cltp 9253 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-pss 3497  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-br 4454  df-opab 4512  df-ltp 9375 This theorem is referenced by:  ltsopr  9422  ltaddpr  9424  ltexprlem7  9432  ltexpri  9433  suplem1pr  9442  suplem2pr  9443
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