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Theorem lerelxr 11325
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 11302 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 4135 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 4029 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff setvar class
Syntax hints:  cdif 3947  wss 3950   × cxp 5682  ccnv 5683  *cxr 11295   < clt 11296  cle 11297
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-ss 3967  df-le 11302
This theorem is referenced by:  lerel  11326  dfle2  13190  dflt2  13191  ledm  18636  lern  18637  letsr  18639  xrsle  21401  znle  21552  leex  42287  i0oii  48824  io1ii  48825
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