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Mirrors > Home > MPE Home > Th. List > otex | Structured version Visualization version GIF version |
Description: An ordered triple of classes is a set. (Contributed by NM, 3-Apr-2015.) |
Ref | Expression |
---|---|
otex | ⊢ 〈𝐴, 𝐵, 𝐶〉 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ot 4525 | . 2 ⊢ 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | |
2 | opex 5322 | . 2 ⊢ 〈〈𝐴, 𝐵〉, 𝐶〉 ∈ V | |
3 | 1, 2 | eqeltri 2829 | 1 ⊢ 〈𝐴, 𝐵, 𝐶〉 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 Vcvv 3398 〈cop 4522 〈cotp 4524 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2710 ax-sep 5167 ax-nul 5174 ax-pr 5296 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-v 3400 df-dif 3846 df-un 3848 df-nul 4212 df-if 4415 df-sn 4517 df-pr 4519 df-op 4523 df-ot 4525 |
This theorem is referenced by: euotd 5370 splval 14202 splcl 14203 idaval 17430 idaf 17435 eldmcoa 17437 coaval 17440 mamufval 21138 msrval 33071 msrf 33075 mapdhval 39361 mndtcco 45825 |
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