Theorem pwid 3736

Description: A set is a member of its power class. Theorem 87 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
pwid.1	⊢ A ∈ V

Assertion

Ref	Expression
pwid	⊢ A ∈ ℘A

Proof of Theorem pwid

Step	Hyp	Ref	Expression
1		pwid.1	. 2 ⊢ A ∈ V
2		pwidg 3735	. 2 ⊢ (A ∈ V → A ∈ ℘A)
3	1, 2	ax-mp 5	1 ⊢ A ∈ ℘A

Syntax hints:   ∈ wcel 1710  Vcvv 2860  ℘cpw 3723

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260  df-pw 3725

This theorem is referenced by: (None)