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Theorem lerelxr 7528
Description: 'Less than or equal' 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 7507 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 3124 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 3054 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff set class
Syntax hints:  cdif 2994  wss 2997   × cxp 4426  ccnv 4427  *cxr 7500   < clt 7501  cle 7502
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 2999  df-in 3003  df-ss 3010  df-le 7507
This theorem is referenced by:  lerel  7529
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