Theorem rspec

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

	Ref	Expression
Hypothesis	rspec.1	⊢ ∀ 𝑥 ∈ 𝐴 𝜑
Assertion	rspec	⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		rspec.1	⊢ ∀ 𝑥 ∈ 𝐴 𝜑
2		rsp	⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ( 𝑥 ∈ 𝐴 → 𝜑 ) )
3	1 2	ax-mp	⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )