Metamath Proof Explorer

Theorem abs1

Description: The absolute value of one is one. (Contributed by David A. Wheeler, 16-Jul-2016)

Ref Expression
Assertion abs1 
|- ( abs ` 1 ) = 1

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 0le1 
 |-  0 <_ 1
3 absid 
 |-  ( ( 1 e. RR /\ 0 <_ 1 ) -> ( abs ` 1 ) = 1 )
4 1 2 3 mp2an 
 |-  ( abs ` 1 ) = 1