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Theorem lerelxr 10698
 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 10675 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 4094 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3987 1 ≤ ⊆ (ℝ* × ℝ*)
 Colors of variables: wff setvar class Syntax hints:   ∖ cdif 3916   ⊆ wss 3919   × cxp 5541  ◡ccnv 5542  ℝ*cxr 10668   < clt 10669   ≤ cle 10670 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-dif 3922  df-in 3926  df-ss 3936  df-le 10675 This theorem is referenced by:  lerel  10699  dfle2  12535  dflt2  12536  ledm  17832  lern  17833  letsr  17835  xrsle  20560  znle  20678
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