Theorem unv 2304

Description: The union of a class with the universal class is the universal class. Exercise 4.10(l) of [Mendelson] p. 231.

Assertion

Ref	Expression
unv	|- (A u. V) = V

Proof of Theorem unv

Step	Hyp	Ref	Expression
1		ssv 2084	. 2 |- (A u. V) (_ V
2		ssun2 2197	. 2 |- V (_ (A u. V)
3	1, 2	eqssi 2081	1 |- (A u. V) = V

Syntax hints:   = wceq 958  Vcvv 1814   u. cun 2048

This theorem is referenced by:  oev2 4168

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-12 970  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

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-in 2054  df-ss 2056

Copyright terms: Public domain