Metamath Proof Explorer


Theorem 3eqtr2i

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006)

Ref Expression
Hypotheses 3eqtr2i.1 A = B
3eqtr2i.2 C = B
3eqtr2i.3 C = D
Assertion 3eqtr2i A = D

Proof

Step Hyp Ref Expression
1 3eqtr2i.1 A = B
2 3eqtr2i.2 C = B
3 3eqtr2i.3 C = D
4 1 2 eqtr4i A = C
5 4 3 eqtri A = D