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Mirrors > Home > MPE Home > Th. List > Mathboxes > brtpid2 | Structured version Visualization version GIF version |
Description: A binary relation involving unordered triples. (Contributed by Scott Fenton, 7-Jun-2016.) |
Ref | Expression |
---|---|
brtpid2 | ⊢ 𝐴{𝐶, 〈𝐴, 𝐵〉, 𝐷}𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 5487 | . . 3 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | 1 | tpid2 4795 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ {𝐶, 〈𝐴, 𝐵〉, 𝐷} |
3 | df-br 5170 | . 2 ⊢ (𝐴{𝐶, 〈𝐴, 𝐵〉, 𝐷}𝐵 ↔ 〈𝐴, 𝐵〉 ∈ {𝐶, 〈𝐴, 𝐵〉, 𝐷}) | |
4 | 2, 3 | mpbir 231 | 1 ⊢ 𝐴{𝐶, 〈𝐴, 𝐵〉, 𝐷}𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2103 {ctp 4652 〈cop 4654 class class class wbr 5169 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2105 ax-9 2113 ax-ext 2705 ax-sep 5320 ax-nul 5327 ax-pr 5450 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-3or 1088 df-3an 1089 df-tru 1540 df-fal 1550 df-ex 1778 df-sb 2065 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3484 df-dif 3973 df-un 3975 df-ss 3987 df-nul 4348 df-if 4549 df-sn 4649 df-pr 4651 df-tp 4653 df-op 4655 df-br 5170 |
This theorem is referenced by: (None) |
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