Metamath Proof Explorer

Theorem unipwr

Description: A class is a subclass of the union of its power class. This theorem is the right-to-left subclass lemma of unipw . The proof of this theorem was automatically generated from unipwrVD using a tools command file , translateMWO.cmd , by translating the proof into its non-virtual deduction form and minimizing it. (Contributed by Alan Sare, 25-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion unipwr A 𝒫 A


Step Hyp Ref Expression
1 vex x V
2 1 snid x x
3 snelpwi x A x 𝒫 A
4 elunii x x x 𝒫 A x 𝒫 A
5 2 3 4 sylancr x A x 𝒫 A
6 5 ssriv A 𝒫 A