Theorem 3eqtr4g

Description: A chained equality inference, useful for converting to definitions. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	3eqtr4g.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	3eqtr4g.2	⊢ 𝐶 = 𝐴
	3eqtr4g.3	⊢ 𝐷 = 𝐵
Assertion	3eqtr4g	⊢ ( 𝜑 → 𝐶 = 𝐷 )

Proof

Step	Hyp	Ref	Expression
1		3eqtr4g.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		3eqtr4g.2	⊢ 𝐶 = 𝐴
3		3eqtr4g.3	⊢ 𝐷 = 𝐵
4	2 1	eqtrid	⊢ ( 𝜑 → 𝐶 = 𝐵 )
5	4 3	eqtr4di	⊢ ( 𝜑 → 𝐶 = 𝐷 )