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Mirrors > Home > MPE Home > Th. List > Mathboxes > brtpid1 | Structured version Visualization version GIF version |
Description: A binary relation involving unordered triplets. (Contributed by Scott Fenton, 7-Jun-2016.) |
Ref | Expression |
---|---|
brtpid1 | ⊢ 𝐴{〈𝐴, 𝐵〉, 𝐶, 𝐷}𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 4932 | . . 3 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | 1 | tpid1 4303 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ {〈𝐴, 𝐵〉, 𝐶, 𝐷} |
3 | df-br 4654 | . 2 ⊢ (𝐴{〈𝐴, 𝐵〉, 𝐶, 𝐷}𝐵 ↔ 〈𝐴, 𝐵〉 ∈ {〈𝐴, 𝐵〉, 𝐶, 𝐷}) | |
4 | 2, 3 | mpbir 221 | 1 ⊢ 𝐴{〈𝐴, 𝐵〉, 𝐶, 𝐷}𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 {ctp 4181 〈cop 4183 class class class wbr 4653 |
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-3or 1038 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-tp 4182 df-op 4184 df-br 4654 |
This theorem is referenced by: (None) |
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