Theorem xrsup

Description: The extended real numbers are unbounded above. (Contributed by Mario Carneiro, 7-May-2016)

	Ref	Expression
Assertion	xrsup	⊢ sup ( ℝ* , ℝ* , < ) = +∞

Proof

Step	Hyp	Ref	Expression
1		ssid	⊢ ℝ* ⊆ ℝ*
2		pnfxr	⊢ +∞ ∈ ℝ*
3		supxrpnf	⊢ ( ( ℝ* ⊆ ℝ* ∧ +∞ ∈ ℝ* ) → sup ( ℝ* , ℝ* , < ) = +∞ )
4	1 2 3	mp2an	⊢ sup ( ℝ* , ℝ* , < ) = +∞