Theorem ressplusg

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

	Ref	Expression
Hypotheses	ressplusg.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
	ressplusg.2	$$⊢\underset{\dot{}}{+}={+}_G$$
Assertion	ressplusg	$$⊢A\in V\to \underset{\dot{}}{+}={+}_H$$

Proof

Step	Hyp	Ref	Expression
1		ressplusg.1	$$⊢H=G{\upharpoonright }_{𝑠}A$$
2		ressplusg.2	$$⊢\underset{\dot{}}{+}={+}_G$$
3		df-plusg	$$⊢{+}_{𝑔}=\mathrm{Slot}2$$
4		2nn	$$⊢2\in \mathbb{N}$$
5		1lt2	$$⊢1<2$$
6	1 2 3 4 5	resslem	$$⊢A\in V\to \underset{\dot{}}{+}={+}_H$$