Theorem eqtr2di

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

	Ref	Expression
Hypotheses	eqtr2di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	eqtr2di.2	⊢ 𝐵 = 𝐶
Assertion	eqtr2di	⊢ ( 𝜑 → 𝐶 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eqtr2di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtr2di.2	⊢ 𝐵 = 𝐶
3	1 2	eqtrdi	⊢ ( 𝜑 → 𝐴 = 𝐶 )
4	3	eqcomd	⊢ ( 𝜑 → 𝐶 = 𝐴 )