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Theorem ltrelpr 9397
Description: Positive real 'less than' is a relation on positive reals. (Contributed by NM, 14-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
ltrelpr

Proof of Theorem ltrelpr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ltp 9384 . 2
2 opabssxp 5079 . 2
31, 2eqsstri 3533 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  e.wcel 1818  C_wss 3475  C.wpss 3476  {copab 4509  X.cxp 5002   cnp 9258   cltp 9262
This theorem is referenced by:  ltexpri  9442  ltaprlem  9443  ltapr  9444  suplem1pr  9451  suplem2pr  9452  supexpr  9453  ltsrpr  9475  ltsosr  9492  mappsrpr  9506
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-opab 4511  df-xp 5010  df-ltp 9384
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