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Theorem lerelxr 9143
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 9128 . 2  |-  <_  =  ( ( RR*  X.  RR* )  \  `'  <  )
2 difss 3476 . 2  |-  ( (
RR*  X.  RR* )  \  `'  <  )  C_  ( RR*  X.  RR* )
31, 2eqsstri 3380 1  |-  <_  C_  ( RR*  X.  RR* )
Colors of variables: wff set class
Syntax hints:    \ cdif 3319    C_ wss 3322    X. cxp 4878   `'ccnv 4879   RR*cxr 9121    < clt 9122    <_ cle 9123
This theorem is referenced by:  lerel  9144  dfle2  10742  dflt2  10743  ledm  14671  lern  14672  letsr  14674  xrsle  16723  znle  16819
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-le 9128
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