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Metamath Proof Explorer

Theorem 3eqtr3i

Description: An inference from three chained equalities. (Contributed by NM, 6-May-1994) (Proof shortened by Andrew Salmon, 25-May-2011)

Ref Expression
Hypotheses 3eqtr3i.1 
|- A = B
3eqtr3i.2 
|- A = C
3eqtr3i.3 
|- B = D
Assertion 3eqtr3i 
|- C = D

Proof

Step Hyp Ref Expression
1 3eqtr3i.1 
 |-  A = B
2 3eqtr3i.2 
 |-  A = C
3 3eqtr3i.3 
 |-  B = D
4 1 2 eqtr3i 
 |-  B = C
5 4 3 eqtr3i 
 |-  C = D