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Theorem lerelxr 10692
Description: "Less than or equal to" is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015.)
Assertion
Ref Expression
lerelxr ≤ ⊆ (ℝ* × ℝ*)

Proof of Theorem lerelxr
StepHypRef Expression
1 df-le 10669 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 4105 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3998 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3930  wss 3933   × cxp 5546  ccnv 5547  *cxr 10662   < clt 10663  cle 10664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-dif 3936  df-in 3940  df-ss 3949  df-le 10669
This theorem is referenced by:  lerel  10693  dfle2  12528  dflt2  12529  ledm  17822  lern  17823  letsr  17825  xrsle  20493  znle  20611
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