Theorem eqtr3id

Description: An equality transitivity deduction. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypotheses	eqtr3id.1	⊢ 𝐵 = 𝐴
	eqtr3id.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	eqtr3id	⊢ ( 𝜑 → 𝐴 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr3id.1	⊢ 𝐵 = 𝐴
2		eqtr3id.2	⊢ ( 𝜑 → 𝐵 = 𝐶 )
3	1	eqcomi	⊢ 𝐴 = 𝐵
4	3 2	syl5eq	⊢ ( 𝜑 → 𝐴 = 𝐶 )