Metamath Proof Explorer


Theorem s3eq2

Description: Equality theorem for a length 3 word for the second symbol. (Contributed by AV, 4-Jan-2022)

Ref Expression
Assertion s3eq2 ⊢ B = D → ⟨“ ABC ”⟩ = ⟨“ ADC ”⟩

Proof

Step Hyp Ref Expression
1 eqidd ⊢ B = D → A = A
2 id ⊢ B = D → B = D
3 eqidd ⊢ B = D → C = C
4 1 2 3 s3eqd ⊢ B = D → ⟨“ ABC ”⟩ = ⟨“ ADC ”⟩