Theorem ressmulr

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

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

Proof

Step	Hyp	Ref	Expression
1		ressmulr.1	⊢ 𝑆 = ( 𝑅 ↾s 𝐴 )
2		ressmulr.2	⊢ · = ( .r ‘ 𝑅 )
3		df-mulr	⊢ .r = Slot 3
4		3nn	⊢ 3 ∈ ℕ
5		1lt3	⊢ 1 < 3
6	1 2 3 4 5	resslem	⊢ ( 𝐴 ∈ 𝑉 → · = ( .r ‘ 𝑆 ) )