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Theorem lerelxr 9697
Description: 'Less than or equal' is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015.)
Assertion
Ref Expression
lerelxr  |-  <_  C_  ( RR*  X.  RR* )

Proof of Theorem lerelxr
StepHypRef Expression
1 df-le 9681 . 2  |-  <_  =  ( ( RR*  X.  RR* )  \  `'  <  )
2 difss 3592 . 2  |-  ( (
RR*  X.  RR* )  \  `'  <  )  C_  ( RR*  X.  RR* )
31, 2eqsstri 3494 1  |-  <_  C_  ( RR*  X.  RR* )
Colors of variables: wff setvar class
Syntax hints:    \ cdif 3433    C_ wss 3436    X. cxp 4847   `'ccnv 4848   RR*cxr 9674    < clt 9675    <_ cle 9676
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-dif 3439  df-in 3443  df-ss 3450  df-le 9681
This theorem is referenced by:  lerel  9698  dfle2  11446  dflt2  11447  ledm  16457  lern  16458  letsr  16460  xrsle  18975  znle  19093
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