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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 4534 | . 2 ⊢ 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | |
2 | opex 5321 | . 2 ⊢ 〈〈𝐴, 𝐵〉, 𝐶〉 ∈ V | |
3 | 1, 2 | eqeltri 2886 | 1 ⊢ 〈𝐴, 𝐵, 𝐶〉 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2111 Vcvv 3441 〈cop 4531 〈cotp 4533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-ot 4534 |
This theorem is referenced by: euotd 5368 splval 14104 splcl 14105 idaval 17310 idaf 17315 eldmcoa 17317 coaval 17320 mamufval 20992 msrval 32898 msrf 32902 mapdhval 39020 |
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