Theorem unv 3579

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 3292	. 2 ⊢ (A ∪ V) ⊆ V
2		ssun2 3428	. 2 ⊢ V ⊆ (A ∪ V)
3	1, 2	eqssi 3289	1 ⊢ (A ∪ V) = V

Syntax hints:   = wceq 1642  Vcvv 2860   ∪ cun 3208

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-un 3215  df-ss 3260

This theorem is referenced by: (None)