Theorem 3eqtr3g

Description: A chained equality inference, useful for converting from definitions. (Contributed by NM, 15-Nov-1994)

	Ref	Expression
Hypotheses	3eqtr3g.1	$$⊢\phi \to A=B$$
	3eqtr3g.2	$$⊢A=C$$
	3eqtr3g.3	$$⊢B=D$$
Assertion	3eqtr3g	$$⊢\phi \to C=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr3g.1	$$⊢\phi \to A=B$$
2		3eqtr3g.2	$$⊢A=C$$
3		3eqtr3g.3	$$⊢B=D$$
4	2 1	eqtr3id	$$⊢\phi \to C=B$$
5	4 3	eqtrdi	$$⊢\phi \to C=D$$