Theorem univ 2915

Description: The union of the universe is the universe. Exercise 4.12(c) of [Mendelson] p. 235.

Assertion

Ref	Expression
univ	|- U.V = V

Proof of Theorem univ

Step	Hyp	Ref	Expression
1		pwv 2506	. . 3 |- P~V = V
2	1	unieqi 2515	. 2 |- U.P~V = U.V
3		unipw 2762	. 2 |- U.P~V = V
4	2, 3	eqtr3 1500	1 |- U.V = V

Syntax hints:   = wceq 958  Vcvv 1814  P~cpw 2405  U.cuni 2507

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-sep 2708  ax-pow 2748

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-v 1815  df-dif 2052  df-un 2053  df-in 2054  df-ss 2056  df-nul 2284  df-pw 2406  df-sn 2416  df-pr 2417  df-uni 2508

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