Theorem eqtr4d

Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)

	Ref	Expression
Hypotheses	eqtr4d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	eqtr4d.2	⊢ ( 𝜑 → 𝐶 = 𝐵 )
Assertion	eqtr4d	⊢ ( 𝜑 → 𝐴 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr4d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtr4d.2	⊢ ( 𝜑 → 𝐶 = 𝐵 )
3	2	eqcomd	⊢ ( 𝜑 → 𝐵 = 𝐶 )
4	1 3	eqtrd	⊢ ( 𝜑 → 𝐴 = 𝐶 )