Theorem rspcevOLD

Description: Obsolete version of rspce as of 12-Dec-2023. Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	rspcv.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	rspcevOLD	⊢ ( ( 𝐴 ∈ 𝐵 ∧ 𝜓 ) → ∃ 𝑥 ∈ 𝐵 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		rspcv.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜓
3	2 1	rspce	⊢ ( ( 𝐴 ∈ 𝐵 ∧ 𝜓 ) → ∃ 𝑥 ∈ 𝐵 𝜑 )