Theorem eqtr4id

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

	Ref	Expression
Hypotheses	eqtr4id.2	⊢ 𝐴 = 𝐵
	eqtr4id.1	⊢ ( 𝜑 → 𝐶 = 𝐵 )
Assertion	eqtr4id	⊢ ( 𝜑 → 𝐴 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr4id.2	⊢ 𝐴 = 𝐵
2		eqtr4id.1	⊢ ( 𝜑 → 𝐶 = 𝐵 )
3	1	eqcomi	⊢ 𝐵 = 𝐴
4	2 3	eqtr2di	⊢ ( 𝜑 → 𝐴 = 𝐶 )