Theorem tpeq1d

Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014)

	Ref	Expression
Hypothesis	tpeq1d.1	|- ( ph -> A = B )
Assertion	tpeq1d	|- ( ph -> { A , C , D } = { B , C , D } )

Proof

Step	Hyp	Ref	Expression
1		tpeq1d.1	|- ( ph -> A = B )
2		tpeq1	|- ( A = B -> { A , C , D } = { B , C , D } )
3	1 2	syl	|- ( ph -> { A , C , D } = { B , C , D } )