Theorem eqtrdi

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

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

Proof

Step	Hyp	Ref	Expression
1		eqtrdi.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtrdi.2	⊢ 𝐵 = 𝐶
3	2	a1i	⊢ ( 𝜑 → 𝐵 = 𝐶 )
4	1 3	eqtrd	⊢ ( 𝜑 → 𝐴 = 𝐶 )