This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3eqtrri

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006) (Proof shortened by Andrew Salmon, 25-May-2011)

Ref Expression
Hypotheses 3eqtri.1 
|- A = B
3eqtri.2 
|- B = C
3eqtri.3 
|- C = D
Assertion 3eqtrri 
|- D = A

Proof

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