Metamath Proof Explorer

Theorem ressxr

Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005)

Ref Expression
Assertion ressxr 
|- RR C_ RR*

Proof

Step Hyp Ref Expression
1 ssun1 
 |-  RR C_ ( RR u. { +oo , -oo } )
2 df-xr 
 |-  RR* = ( RR u. { +oo , -oo } )
3 1 2 sseqtrri 
 |-  RR C_ RR*