Theorem resvplusg

Description: +g is unaffected by scalar restriction. (Contributed by Thierry Arnoux, 6-Sep-2018)

	Ref	Expression
Hypotheses	resvbas.1	⊢ 𝐻 = ( 𝐺 ↾v 𝐴 )
	resvplusg.2	⊢ + = ( +g ‘ 𝐺 )
Assertion	resvplusg	⊢ ( 𝐴 ∈ 𝑉 → + = ( +g ‘ 𝐻 ) )

Proof

Step	Hyp	Ref	Expression
1		resvbas.1	⊢ 𝐻 = ( 𝐺 ↾v 𝐴 )
2		resvplusg.2	⊢ + = ( +g ‘ 𝐺 )
3		df-plusg	⊢ +g = Slot 2
4		2nn	⊢ 2 ∈ ℕ
5		2re	⊢ 2 ∈ ℝ
6		2lt5	⊢ 2 < 5
7	5 6	ltneii	⊢ 2 ≠ 5
8	1 2 3 4 7	resvlem	⊢ ( 𝐴 ∈ 𝑉 → + = ( +g ‘ 𝐻 ) )