Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > 0un | Structured version Visualization version GIF version |
Description: The union of the empty set with a class is itself. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
0un | ⊢ (∅ ∪ 𝐴) = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 3719 | . 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅) | |
2 | un0 3919 | . 2 ⊢ (𝐴 ∪ ∅) = 𝐴 | |
3 | 1, 2 | eqtri 2632 | 1 ⊢ (∅ ∪ 𝐴) = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∪ cun 3538 ∅c0 3874 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 |
This theorem is referenced by: fiiuncl 38259 founiiun0 38372 meadjun 39355 caragenuncllem 39402 carageniuncllem1 39411 hoidmvle 39490 |
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