Theorem 3eqtr3d

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-1995) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr3d.1	$$⊢\phi \to A=B$$
	3eqtr3d.2	$$⊢\phi \to A=C$$
	3eqtr3d.3	$$⊢\phi \to B=D$$
Assertion	3eqtr3d	$$⊢\phi \to C=D$$

Proof

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