Theorem sgn1

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

	Ref	Expression
Assertion	sgn1	$$⊢\mathrm{sgn}\left(1\right)=1$$

Proof

Step	Hyp	Ref	Expression
1		1xr	$$⊢1\in {ℝ}^{*}$$
2		0lt1	$$⊢0<1$$
3		sgnp	$$⊢\left(1\in {ℝ}^{*}\wedge 0<1\right)\to \mathrm{sgn}\left(1\right)=1$$
4	1 2 3	mp2an	$$⊢\mathrm{sgn}\left(1\right)=1$$