Theorem snelpwiOLD

Description: Obsolete version of snelpwi as of 17-Jan-2025. (Contributed by NM, 28-May-1995) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	snelpwiOLD	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ∈ 𝒫 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		snssi	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ⊆ 𝐵 )
2		snex	⊢ { 𝐴 } ∈ V
3	2	elpw	⊢ ( { 𝐴 } ∈ 𝒫 𝐵 ↔ { 𝐴 } ⊆ 𝐵 )
4	1 3	sylibr	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ∈ 𝒫 𝐵 )