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		plusgid	⊢ +g = Slot ( +g ‘ ndx )
4		basendxnplusgndx	⊢ ( Base ‘ ndx ) ≠ ( +g ‘ ndx )
5	4	necomi	⊢ ( +g ‘ ndx ) ≠ ( Base ‘ ndx )
6	1 2 3 5	resseqnbas	⊢ ( 𝐴 ∈ 𝑉 → + = ( +g ‘ 𝐻 ) )