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Theorem lerelxr 11223
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 11200 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 4092 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3979 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3908  wss 3911   × cxp 5632  ccnv 5633  *cxr 11193   < clt 11194  cle 11195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-in 3918  df-ss 3928  df-le 11200
This theorem is referenced by:  lerel  11224  dfle2  13072  dflt2  13073  ledm  18484  lern  18485  letsr  18487  xrsle  20833  znle  20955  i0oii  47038  io1ii  47039
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