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Metamath Proof Explorer

Theorem 3eqtri

Description: An inference from three chained equalities. (Contributed by NM, 29-Aug-1993)

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

Proof

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