Theorem rspec

Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994)

	Ref	Expression
Hypothesis	rspec.1	$$⊢\forall x\in A\phi$$
Assertion	rspec	$$⊢x\in A\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		rspec.1	$$⊢\forall x\in A\phi$$
2		rsp	$$⊢\forall x\in A\phi \to \left(x\in A\to \phi \right)$$
3	1 2	ax-mp	$$⊢x\in A\to \phi$$