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Metamath Proof Explorer

Theorem 3eqtrri

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

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

Proof

Step Hyp Ref Expression
1 3eqtri.1 ⊢ 𝐴 = 𝐵
2 3eqtri.2 ⊢ 𝐵 = 𝐶
3 3eqtri.3 ⊢ 𝐶 = 𝐷
4 1 2 eqtri ⊢ 𝐴 = 𝐶
5 4 3 eqtr2i ⊢ 𝐷 = 𝐴