Theorem tpeq1d

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

	Ref	Expression
Hypothesis	tpeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	tpeq1d	⊢ ( 𝜑 → { 𝐴 , 𝐶 , 𝐷 } = { 𝐵 , 𝐶 , 𝐷 } )

Proof

Step	Hyp	Ref	Expression
1		tpeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		tpeq1	⊢ ( 𝐴 = 𝐵 → { 𝐴 , 𝐶 , 𝐷 } = { 𝐵 , 𝐶 , 𝐷 } )
3	1 2	syl	⊢ ( 𝜑 → { 𝐴 , 𝐶 , 𝐷 } = { 𝐵 , 𝐶 , 𝐷 } )