Metamath Proof Explorer

Theorem sgn1

Description: The signum of 1 is 1. (Contributed by David A. Wheeler, 26-Jun-2016)

Ref Expression
Assertion sgn1 
|- ( sgn ` 1 ) = 1

Proof

Step Hyp Ref Expression
1 1xr 
 |-  1 e. RR*
2 0lt1 
 |-  0 < 1
3 sgnp 
 |-  ( ( 1 e. RR* /\ 0 < 1 ) -> ( sgn ` 1 ) = 1 )
4 1 2 3 mp2an 
 |-  ( sgn ` 1 ) = 1