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Mirrors > Home > MPE Home > Th. List > unisnv | Structured version Visualization version GIF version |
Description: A set equals the union of its singleton (setvar case). (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
unisnv | ⊢ ∪ {𝑥} = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3479 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | unisn 4926 | 1 ⊢ ∪ {𝑥} = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 {csn 4624 ∪ cuni 4904 |
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 3477 df-un 3951 df-in 3953 df-ss 3963 df-sn 4625 df-pr 4627 df-uni 4905 |
This theorem is referenced by: uniintsn 4987 uniabio 6502 iotauni2 6504 opabiotafun 6961 onuninsuci 7816 en1b 9011 fin1a2lem10 10391 incexclem 15769 sylow2a 19471 1stckgenlem 23026 alexsubALTlem3 23522 ptcmplem2 23526 icccmplem1 24307 unidifsnel 31738 unidifsnne 31739 disjabrex 31779 disjabrexf 31780 fiunelcarsg 33246 carsgclctunlem1 33247 fobigcup 34803 mbfresfi 36439 |
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