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Theorem lerelxr 10139
Description: 'Less than or equal' 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 10118 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 3770 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3668 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3604  wss 3607   × cxp 5141  ccnv 5142  *cxr 10111   < clt 10112  cle 10113
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-dif 3610  df-in 3614  df-ss 3621  df-le 10118
This theorem is referenced by:  lerel  10140  dfle2  12018  dflt2  12019  ledm  17271  lern  17272  letsr  17274  xrsle  19814  znle  19932
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