Theorem 3eqtr2d

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006)

	Ref	Expression
Hypotheses	3eqtr2d.1	$$⊢\phi \to A=B$$
	3eqtr2d.2	$$⊢\phi \to C=B$$
	3eqtr2d.3	$$⊢\phi \to C=D$$
Assertion	3eqtr2d	$$⊢\phi \to A=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr2d.1	$$⊢\phi \to A=B$$
2		3eqtr2d.2	$$⊢\phi \to C=B$$
3		3eqtr2d.3	$$⊢\phi \to C=D$$
4	1 2	eqtr4d	$$⊢\phi \to A=C$$
5	4 3	eqtrd	$$⊢\phi \to A=D$$