Theorem brtpid1

Description: A binary relation involving unordered triples. (Contributed by Scott Fenton, 7-Jun-2016)

	Ref	Expression
Assertion	brtpid1	$$⊢A\left\{⟨A,B⟩,C,D\right\}B$$

Proof

Step	Hyp	Ref	Expression
1		opex	$$⊢⟨A,B⟩\in \mathrm{V}$$
2	1	tpid1	$$⊢⟨A,B⟩\in \left\{⟨A,B⟩,C,D\right\}$$
3		df-br	$$⊢A\left\{⟨A,B⟩,C,D\right\}B\leftrightarrow ⟨A,B⟩\in \left\{⟨A,B⟩,C,D\right\}$$
4	2 3	mpbir	$$⊢A\left\{⟨A,B⟩,C,D\right\}B$$