Theorem eqtr3di

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

	Ref	Expression
Hypotheses	eqtr3di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	eqtr3di.2	⊢ 𝐴 = 𝐶
Assertion	eqtr3di	⊢ ( 𝜑 → 𝐵 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr3di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtr3di.2	⊢ 𝐴 = 𝐶
3	2	eqcomi	⊢ 𝐶 = 𝐴
4	3 1	eqtr2id	⊢ ( 𝜑 → 𝐵 = 𝐶 )