Theorem 3eqtr4g

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

	Ref	Expression
Hypotheses	3eqtr4g.1	$$⊢\phi \to A=B$$
	3eqtr4g.2	$$⊢C=A$$
	3eqtr4g.3	$$⊢D=B$$
Assertion	3eqtr4g	$$⊢\phi \to C=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr4g.1	$$⊢\phi \to A=B$$
2		3eqtr4g.2	$$⊢C=A$$
3		3eqtr4g.3	$$⊢D=B$$
4	2 1	syl5eq	$$⊢\phi \to C=B$$
5	4 3	eqtr4di	$$⊢\phi \to C=D$$