Theorem tpass

Description: Split off the first element of an unordered triple. (Contributed by Mario Carneiro, 5-Jan-2016)

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

Proof

Step	Hyp	Ref	Expression
1		df-tp	$$⊢\left\{B,C,A\right\}=\left\{B,C\right\}\cup \left\{A\right\}$$
2		tprot	$$⊢\left\{A,B,C\right\}=\left\{B,C,A\right\}$$
3		uncom	$$⊢\left\{A\right\}\cup \left\{B,C\right\}=\left\{B,C\right\}\cup \left\{A\right\}$$
4	1 2 3	3eqtr4i	$$⊢\left\{A,B,C\right\}=\left\{A\right\}\cup \left\{B,C\right\}$$