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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 4186 | . 2 ⊢ 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | |
2 | opex 4932 | . 2 ⊢ 〈〈𝐴, 𝐵〉, 𝐶〉 ∈ V | |
3 | 1, 2 | eqeltri 2697 | 1 ⊢ 〈𝐴, 𝐵, 𝐶〉 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 Vcvv 3200 〈cop 4183 〈cotp 4185 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-ot 4186 |
This theorem is referenced by: euotd 4975 splval 13502 splcl 13503 idaval 16708 idaf 16713 eldmcoa 16715 coaval 16718 mamufval 20191 msrval 31435 msrf 31439 mapdhval 37013 |
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