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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 3993 | . 2 ⊢ (𝐴 ∪ V) ⊆ V | |
2 | ssun2 4151 | . 2 ⊢ V ⊆ (𝐴 ∪ V) | |
3 | 1, 2 | eqssi 3985 | 1 ⊢ (𝐴 ∪ V) = V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 Vcvv 3496 ∪ cun 3936 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-v 3498 df-un 3943 df-in 3945 df-ss 3954 |
This theorem is referenced by: oev2 8150 |
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