Theorem pwv 2492

Description: The power class of the universe is the universe. Exercise 4.12(d) of [Mendelson] p. 235.

Assertion

Ref	Expression
pwv	|- P~V = V

Proof of Theorem pwv

Step	Hyp	Ref	Expression
1		ssv 2071	. . . 4 |- x (_ V
2		visset 1804	. . . . 5 |- x e. V
3	2	elpw 2394	. . . 4 |- (x e. P~V <-> x (_ V)
4	1, 3	mpbir 190	. . 3 |- x e. P~V
5	4, 2	2th 716	. 2 |- (x e. P~V <-> x e. V)
6	5	eqriv 1467	1 |- P~V = V

Syntax hints:   = wceq 953   e. wcel 955  Vcvv 1802   (_ wss 2037  P~cpw 2391

This theorem is referenced by:  univ 2899  ncanth 3893

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-in 2041  df-ss 2043  df-pw 2392

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