This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pwex

Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypothesis pwex.1 ⊢ 𝐴 ∈ V
Assertion pwex 𝒫 𝐴 ∈ V

Proof

Step Hyp Ref Expression
1 pwex.1 ⊢ 𝐴 ∈ V
2 pwexg ⊢ ( 𝐴 ∈ V → 𝒫 𝐴 ∈ V )
3 1 2 ax-mp ⊢ 𝒫 𝐴 ∈ V