Theorem ressplusg

Description: +g is unaffected by restriction. (Contributed by Stefan O'Rear, 27-Nov-2014)

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

Proof

Step	Hyp	Ref	Expression
1		ressplusg.1	⊢ 𝐻 = ( 𝐺 ↾s 𝐴 )
2		ressplusg.2	⊢ + = ( +g ‘ 𝐺 )
3		df-plusg	⊢ +g = Slot 2
4		2nn	⊢ 2 ∈ ℕ
5		1lt2	⊢ 1 < 2
6	1 2 3 4 5	resslem	⊢ ( 𝐴 ∈ 𝑉 → + = ( +g ‘ 𝐻 ) )