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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