Theorem tpcomb

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015)

	Ref	Expression
Assertion	tpcomb	$$⊢\left\{A,B,C\right\}=\left\{A,C,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		tpcoma	$$⊢\left\{B,C,A\right\}=\left\{C,B,A\right\}$$
2		tprot	$$⊢\left\{A,B,C\right\}=\left\{B,C,A\right\}$$
3		tprot	$$⊢\left\{A,C,B\right\}=\left\{C,B,A\right\}$$
4	1 2 3	3eqtr4i	$$⊢\left\{A,B,C\right\}=\left\{A,C,B\right\}$$