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Theorem lerelxr 8904
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 8889 . 2  |-  <_  =  ( ( RR*  X.  RR* )  \  `'  <  )
2 difss 3316 . 2  |-  ( (
RR*  X.  RR* )  \  `'  <  )  C_  ( RR*  X.  RR* )
31, 2eqsstri 3221 1  |-  <_  C_  ( RR*  X.  RR* )
Colors of variables: wff set class
Syntax hints:    \ cdif 3162    C_ wss 3165    X. cxp 4703   `'ccnv 4704   RR*cxr 8882    < clt 8883    <_ cle 8884
This theorem is referenced by:  lerel  8905  dfle2  10497  dflt2  10498  ledm  14362  lern  14363  letsr  14365  xrsle  16410  znle  16506  mlteqer  25720
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-le 8889
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