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Theorem lerelxr 11195
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 11172 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 4088 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3980 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3898  wss 3901   × cxp 5622  ccnv 5623  *cxr 11165   < clt 11166  cle 11167
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-dif 3904  df-ss 3918  df-le 11172
This theorem is referenced by:  lerel  11196  dfle2  13061  dflt2  13062  xrsle  17525  ledm  18513  lern  18514  letsr  18516  znle  21491  leex  42497  i0oii  49161  io1ii  49162
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