Theorem unv 3507

Description: The union of a class with the universal class is the universal class. Exercise 4.10(l) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.)

Assertion

Ref	Expression
unv	⊢ (𝐴 ∪ V) = V

Proof of Theorem unv

Step	Hyp	Ref	Expression
1		ssv 3224	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 3346	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3218	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1373  Vcvv 2777   ∪ cun 3173

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2779  df-un 3179  df-in 3181  df-ss 3188

This theorem is referenced by: (None)