Theorem rspe

Description: Restricted specialization. (Contributed by NM, 12-Oct-1999)

	Ref	Expression
Assertion	rspe	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → ∃ 𝑥 ∈ 𝐴 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		19.8a	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
2		df-rex	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 ↔ ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
3	1 2	sylibr	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → ∃ 𝑥 ∈ 𝐴 𝜑 )