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Metamath Proof Explorer

Theorem 3eqtr4i

Description: An inference from three chained equalities. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 25-May-2011)

Ref Expression
Hypotheses 3eqtr4i.1 ⊢ A = B
3eqtr4i.2 ⊢ C = A
3eqtr4i.3 ⊢ D = B
Assertion 3eqtr4i ⊢ C = D

Proof

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