Theorem eqtr3d

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

	Ref	Expression
Hypotheses	eqtr3d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	eqtr3d.2	⊢ ( 𝜑 → 𝐴 = 𝐶 )
Assertion	eqtr3d	⊢ ( 𝜑 → 𝐵 = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqtr3d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqtr3d.2	⊢ ( 𝜑 → 𝐴 = 𝐶 )
3	1	eqcomd	⊢ ( 𝜑 → 𝐵 = 𝐴 )
4	3 2	eqtrd	⊢ ( 𝜑 → 𝐵 = 𝐶 )