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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 4635 | . 2 ⊢ 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | |
| 2 | opex 5469 | . 2 ⊢ 〈〈𝐴, 𝐵〉, 𝐶〉 ∈ V | |
| 3 | 1, 2 | eqeltri 2837 | 1 ⊢ 〈𝐴, 𝐵, 𝐶〉 ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 Vcvv 3480 〈cop 4632 〈cotp 4634 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-ot 4635 |
| This theorem is referenced by: euotd 5518 ralxp3f 8162 xpord3lem 8174 xpord3pred 8177 splval 14789 splcl 14790 idaval 18103 idaf 18108 eldmcoa 18110 coaval 18113 mamufval 22396 msrval 35543 msrf 35547 mapdhval 41726 mndtcco 49182 |
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