Theorem 3eqtrd

Description: A deduction from three chained equalities. (Contributed by NM, 29-Oct-1995)

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

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	2 3	eqtrd	$$⊢\phi \to B=D$$
5	1 4	eqtrd	$$⊢\phi \to A=D$$