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Mirrors > Home > MPE Home > Th. List > unv | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
unv | ⊢ (𝐴 ∪ V) = V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3969 | . 2 ⊢ (𝐴 ∪ V) ⊆ V | |
2 | ssun2 4134 | . 2 ⊢ V ⊆ (𝐴 ∪ V) | |
3 | 1, 2 | eqssi 3961 | 1 ⊢ (𝐴 ∪ V) = V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 Vcvv 3444 ∪ cun 3909 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-un 3916 df-in 3918 df-ss 3928 |
This theorem is referenced by: oev2 8470 |
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