Theorem ressstarv

Description: *r is unaffected by restriction. (Contributed by Mario Carneiro, 9-Oct-2015)

	Ref	Expression
Hypotheses	ressmulr.1	⊢ 𝑆 = ( 𝑅 ↾s 𝐴 )
	ressstarv.2	⊢ ∗ = ( *𝑟 ‘ 𝑅 )
Assertion	ressstarv	⊢ ( 𝐴 ∈ 𝑉 → ∗ = ( *𝑟 ‘ 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		ressmulr.1	⊢ 𝑆 = ( 𝑅 ↾s 𝐴 )
2		ressstarv.2	⊢ ∗ = ( *𝑟 ‘ 𝑅 )
3		starvid	⊢ *𝑟 = Slot ( *𝑟 ‘ ndx )
4		starvndxnbasendx	⊢ ( *𝑟 ‘ ndx ) ≠ ( Base ‘ ndx )
5	1 2 3 4	resseqnbas	⊢ ( 𝐴 ∈ 𝑉 → ∗ = ( *𝑟 ‘ 𝑆 ) )