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Metamath Proof Explorer

Theorem 3eqtr2i

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006)

Ref Expression
Hypotheses 3eqtr2i.1 ⊢ A = B
3eqtr2i.2 ⊢ C = B
3eqtr2i.3 ⊢ C = D
Assertion 3eqtr2i ⊢ A = D

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 eqtri ⊢ A = D