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Metamath Proof Explorer

Theorem sselpwd

Description: Elementhood to a power set. (Contributed by Thierry Arnoux, 18-May-2020)

Ref Expression
Hypotheses sselpwd.1 ⊢ ( 𝜑 → 𝐵 ∈ 𝑉 )
sselpwd.2 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
Assertion sselpwd ( 𝜑 → 𝐴 ∈ 𝒫 𝐵 )

Proof

Step Hyp Ref Expression
1 sselpwd.1 ⊢ ( 𝜑 → 𝐵 ∈ 𝑉 )
2 sselpwd.2 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
3 1 2 ssexd ⊢ ( 𝜑 → 𝐴 ∈ V )
4 3 2 elpwd ⊢ ( 𝜑 → 𝐴 ∈ 𝒫 𝐵 )