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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 5457 | . . 3 ⊢ ⟨𝐴, 𝐵⟩ ∈ V | |
2 | 1 | tpid2 4769 | . 2 ⊢ ⟨𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷} |
3 | df-br 5142 | . 2 ⊢ (𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷}) | |
4 | 2, 3 | mpbir 230 | 1 ⊢ 𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2098 {ctp 4627 ⟨cop 4629 class class class wbr 5141 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pr 5420 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-v 3470 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-sn 4624 df-pr 4626 df-tp 4628 df-op 4630 df-br 5142 |
This theorem is referenced by: (None) |
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