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Theorem rexrd 6872
Description: A standard real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rexrd.1  RR
Assertion
Ref Expression
rexrd  RR*

Proof of Theorem rexrd
StepHypRef Expression
1 ressxr 6866 . 2  RR  C_  RR*
2 rexrd.1 . 2  RR
31, 2sseldi 2937 1  RR*
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   RRcr 6710   RR*cxr 6856
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-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-un 2916  df-in 2918  df-ss 2925  df-xr 6861
This theorem is referenced by:  rpxr  8365  rpxrd  8398  xnegcl  8515  iooshf  8591  icoshftf1o  8629
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