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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