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Metamath Proof Explorer

Theorem 3eqtr2ri

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

Ref Expression
Hypotheses 3eqtr2i.1 
|- A = B
3eqtr2i.2 
|- C = B
3eqtr2i.3 
|- C = D
Assertion 3eqtr2ri 
|- D = A

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 eqtr2i 
 |-  D = A