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Metamath Proof Explorer

Theorem velpw

Description: Setvar variable membership in a power class. (Contributed by David A. Wheeler, 8-Dec-2018)

Ref Expression
Assertion velpw ( 𝑥 ∈ 𝒫 𝐴 ↔ 𝑥 ⊆ 𝐴 )

Proof

Step Hyp Ref Expression
1 vex ⊢ 𝑥 ∈ V
2 1 elpw ⊢ ( 𝑥 ∈ 𝒫 𝐴 ↔ 𝑥 ⊆ 𝐴 )