Theorem sgnpnf

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

	Ref	Expression
Assertion	sgnpnf	⊢ ( sgn ‘ +∞ ) = 1

Proof

Step	Hyp	Ref	Expression
1		pnfxr	⊢ +∞ ∈ ℝ*
2		0ltpnf	⊢ 0 < +∞
3		sgnp	⊢ ( ( +∞ ∈ ℝ* ∧ 0 < +∞ ) → ( sgn ‘ +∞ ) = 1 )
4	1 2 3	mp2an	⊢ ( sgn ‘ +∞ ) = 1