Theorem eqtr2id

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

	Ref	Expression
Hypotheses	eqtr2id.1	⊢ 𝐴 = 𝐵
	eqtr2id.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	eqtr2id	⊢ ( 𝜑 → 𝐶 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eqtr2id.1	⊢ 𝐴 = 𝐵
2		eqtr2id.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
3	1 2	syl5eq	⊢ ( 𝜑 → 𝐴 = 𝐶 )
4	3	eqcomd	⊢ ( 𝜑 → 𝐶 = 𝐴 )