Theorem 3eqtr3a

Description: A chained equality inference, useful for converting from definitions. (Contributed by Mario Carneiro, 6-Nov-2015)

	Ref	Expression
Hypotheses	3eqtr3a.1	$$⊢A=B$$
	3eqtr3a.2	$$⊢\phi \to A=C$$
	3eqtr3a.3	$$⊢\phi \to B=D$$
Assertion	3eqtr3a	$$⊢\phi \to C=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr3a.1	$$⊢A=B$$
2		3eqtr3a.2	$$⊢\phi \to A=C$$
3		3eqtr3a.3	$$⊢\phi \to B=D$$
4	1 3	syl5eq	$$⊢\phi \to A=D$$
5	2 4	eqtr3d	$$⊢\phi \to C=D$$