Metamath Proof Explorer

Theorem rele2

Description: The ordering relation of the field of reals. (Contributed by Thierry Arnoux, 21-Jan-2018)

Ref Expression
Assertion rele2 
|- <_ = ( le ` RRfld )

Proof

Step Hyp Ref Expression
1 reex 
 |-  RR e. _V
2 df-refld 
 |-  RRfld = ( CCfld |`s RR )
3 cnfldle 
 |-  <_ = ( le ` CCfld )
4 2 3 ressle 
 |-  ( RR e. _V -> <_ = ( le ` RRfld ) )
5 1 4 ax-mp 
 |-  <_ = ( le ` RRfld )