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 ∈ ℝ*
2		0lt1	⊢ 0 < 1
3		sgnp	⊢ ( ( 1 ∈ ℝ* ∧ 0 < 1 ) → ( sgn ‘ 1 ) = 1 )
4	1 2 3	mp2an	⊢ ( sgn ‘ 1 ) = 1