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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 3851 | . 2 ⊢ (𝐴 ∪ V) ⊆ V | |
2 | ssun2 4005 | . 2 ⊢ V ⊆ (𝐴 ∪ V) | |
3 | 1, 2 | eqssi 3844 | 1 ⊢ (𝐴 ∪ V) = V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1658 Vcvv 3415 ∪ cun 3797 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-ext 2804 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-clab 2813 df-cleq 2819 df-clel 2822 df-nfc 2959 df-v 3417 df-un 3804 df-in 3806 df-ss 3813 |
This theorem is referenced by: oev2 7871 |
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