Metamath Proof Explorer


Theorem lswccat0lsw

Description: The last symbol of a word concatenated with the empty word is the last symbol of the word. (Contributed by AV, 22-Oct-2018) (Proof shortened by AV, 1-May-2020)

Ref Expression
Assertion lswccat0lsw ( 𝑊 ∈ Word 𝑉 → ( lastS ‘ ( 𝑊 ++ ∅ ) ) = ( lastS ‘ 𝑊 ) )

Proof

Step Hyp Ref Expression
1 ccatrid ( 𝑊 ∈ Word 𝑉 → ( 𝑊 ++ ∅ ) = 𝑊 )
2 1 fveq2d ( 𝑊 ∈ Word 𝑉 → ( lastS ‘ ( 𝑊 ++ ∅ ) ) = ( lastS ‘ 𝑊 ) )