Theorem 3eqtr4d

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

	Ref	Expression
Hypotheses	3eqtr4d.1	$$⊢\phi \to A=B$$
	3eqtr4d.2	$$⊢\phi \to C=A$$
	3eqtr4d.3	$$⊢\phi \to D=B$$
Assertion	3eqtr4d	$$⊢\phi \to C=D$$

Proof

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