Theorem eqtrid

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

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

Proof

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