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Theorem lerelxr 10359
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 10338 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 3901 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3797 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3731  wss 3734   × cxp 5277  ccnv 5278  *cxr 10331   < clt 10332  cle 10333
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-dif 3737  df-in 3741  df-ss 3748  df-le 10338
This theorem is referenced by:  lerel  10360  dfle2  12185  dflt2  12186  ledm  17504  lern  17505  letsr  17507  xrsle  20053  znle  20171
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