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

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