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Theorem lerelxr 8888
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 8873 . 2  |-  <_  =  ( ( RR*  X.  RR* )  \  `'  <  )
2 difss 3303 . 2  |-  ( (
RR*  X.  RR* )  \  `'  <  )  C_  ( RR*  X.  RR* )
31, 2eqsstri 3208 1  |-  <_  C_  ( RR*  X.  RR* )
Colors of variables: wff set class
Syntax hints:    \ cdif 3149    C_ wss 3152    X. cxp 4687   `'ccnv 4688   RR*cxr 8866    < clt 8867    <_ cle 8868
This theorem is referenced by:  lerel  8889  dfle2  10481  dflt2  10482  ledm  14346  lern  14347  letsr  14349  xrsle  16394  znle  16490  mlteqer  25617
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-le 8873
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