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Theorem lerelxr 6879
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 6863 . 2 ≤ = ((ℝ* × ℝ*) ∖ < )
2 difss 3064 . 2 ((ℝ* × ℝ*) ∖ < ) ⊆ (ℝ* × ℝ*)
31, 2eqsstri 2969 1 ≤ ⊆ (ℝ* × ℝ*)
Colors of variables: wff set class
Syntax hints:  cdif 2908  wss 2911   × cxp 4286  ccnv 4287  *cxr 6856   < clt 6857  cle 6858
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925  df-le 6863
This theorem is referenced by:  lerel  6880
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