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Mirrors > Home > MPE Home > Th. List > Mathboxes > brtpid3 | Structured version Visualization version GIF version |
Description: A binary relation involving unordered triplets. (Contributed by Scott Fenton, 7-Jun-2016.) |
Ref | Expression |
---|---|
brtpid3 | ⊢ 𝐴{𝐶, 𝐷, 〈𝐴, 𝐵〉}𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 5347 | . . 3 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | 1 | tpid3 4701 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ {𝐶, 𝐷, 〈𝐴, 𝐵〉} |
3 | df-br 5058 | . 2 ⊢ (𝐴{𝐶, 𝐷, 〈𝐴, 𝐵〉}𝐵 ↔ 〈𝐴, 𝐵〉 ∈ {𝐶, 𝐷, 〈𝐴, 𝐵〉}) | |
4 | 2, 3 | mpbir 233 | 1 ⊢ 𝐴{𝐶, 𝐷, 〈𝐴, 𝐵〉}𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2108 {ctp 4563 〈cop 4565 class class class wbr 5057 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1083 df-3an 1084 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-v 3495 df-dif 3937 df-un 3939 df-in 3941 df-ss 3950 df-nul 4290 df-if 4466 df-sn 4560 df-pr 4562 df-tp 4564 df-op 4566 df-br 5058 |
This theorem is referenced by: (None) |
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