Theorem 3eqtrrd

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006) (Proof shortened by Andrew Salmon, 25-May-2011)

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

Proof

Step	Hyp	Ref	Expression
1		3eqtrd.1	$$⊢\phi \to A=B$$
2		3eqtrd.2	$$⊢\phi \to B=C$$
3		3eqtrd.3	$$⊢\phi \to C=D$$
4	1 2	eqtrd	$$⊢\phi \to A=C$$
5	4 3	eqtr2d	$$⊢\phi \to D=A$$