Theorem 3eqtr4a

Description: A chained equality inference, useful for converting to definitions. (Contributed by NM, 2-Feb-2007) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr4a.1	$$⊢A=B$$
	3eqtr4a.2	$$⊢\phi \to C=A$$
	3eqtr4a.3	$$⊢\phi \to D=B$$
Assertion	3eqtr4a	$$⊢\phi \to C=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr4a.1	$$⊢A=B$$
2		3eqtr4a.2	$$⊢\phi \to C=A$$
3		3eqtr4a.3	$$⊢\phi \to D=B$$
4	2 1	syl6eq	$$⊢\phi \to C=B$$
5	4 3	eqtr4d	$$⊢\phi \to C=D$$