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		plusgid	$$⊢{+}_{𝑔}=\mathrm{Slot}{+}_{\mathrm{ndx}}$$
4		basendxnplusgndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}\ne {+}_{\mathrm{ndx}}$$
5	4	necomi	$$⊢{+}_{\mathrm{ndx}}\ne {\mathrm{Base}}_{\mathrm{ndx}}$$
6	1 2 3 5	resseqnbas	$$⊢A\in V\to \underset{\dot{}}{+}={+}_H$$