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Mirrors > Home > MPE Home > Th. List > Mathboxes > brtpid1 | Structured version Visualization version GIF version |
Description: A binary relationship 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 4859 | . . 3 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | 1 | tpid1 4246 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ {〈𝐴, 𝐵〉, 𝐶, 𝐷} |
3 | df-br 4584 | . 2 ⊢ (𝐴{〈𝐴, 𝐵〉, 𝐶, 𝐷}𝐵 ↔ 〈𝐴, 𝐵〉 ∈ {〈𝐴, 𝐵〉, 𝐶, 𝐷}) | |
4 | 2, 3 | mpbir 220 | 1 ⊢ 𝐴{〈𝐴, 𝐵〉, 𝐶, 𝐷}𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 {ctp 4129 〈cop 4131 class class class wbr 4583 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-tp 4130 df-op 4132 df-br 4584 |
This theorem is referenced by: (None) |
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