Theorem xrge0plusg

Description: The additive law of the extended nonnegative real numbers monoid is the addition in the extended real numbers. (Contributed by Thierry Arnoux, 20-Mar-2017)

	Ref	Expression
Assertion	xrge0plusg	⊢ +𝑒 = ( +g ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) )

Proof

Step	Hyp	Ref	Expression
1		ovex	⊢ ( 0 [,] +∞ ) ∈ V
2		eqid	⊢ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) = ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) )
3		xrsadd	⊢ +𝑒 = ( +g ‘ ℝ*𝑠 )
4	2 3	ressplusg	⊢ ( ( 0 [,] +∞ ) ∈ V → +𝑒 = ( +g ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) ) )
5	1 4	ax-mp	⊢ +𝑒 = ( +g ‘ ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) )