Theorem tpeq2

Description: Equality theorem for unordered triples. (Contributed by NM, 13-Sep-2011)

	Ref	Expression
Assertion	tpeq2	$$⊢A=B\to \left\{C,A,D\right\}=\left\{C,B,D\right\}$$

Proof

Step	Hyp	Ref	Expression
1		preq2	$$⊢A=B\to \left\{C,A\right\}=\left\{C,B\right\}$$
2	1	uneq1d	$$⊢A=B\to \left\{C,A\right\}\cup \left\{D\right\}=\left\{C,B\right\}\cup \left\{D\right\}$$
3		df-tp	$$⊢\left\{C,A,D\right\}=\left\{C,A\right\}\cup \left\{D\right\}$$
4		df-tp	$$⊢\left\{C,B,D\right\}=\left\{C,B\right\}\cup \left\{D\right\}$$
5	2 3 4	3eqtr4g	$$⊢A=B\to \left\{C,A,D\right\}=\left\{C,B,D\right\}$$