Theorem eqtr4di

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

	Ref	Expression
Hypotheses	eqtr4di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	eqtr4di.2	⊢ 𝐶 = 𝐵
Assertion	eqtr4di	⊢ ( 𝜑 → 𝐴 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr4di.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtr4di.2	⊢ 𝐶 = 𝐵
3	2	eqcomi	⊢ 𝐵 = 𝐶
4	1 3	eqtrdi	⊢ ( 𝜑 → 𝐴 = 𝐶 )