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 e. Word V -> ( lastS ` ( W ++ (/) ) ) = ( lastS ` W ) )

Proof

Step Hyp Ref Expression
1 ccatrid
 |-  ( W e. Word V -> ( W ++ (/) ) = W )
2 1 fveq2d
 |-  ( W e. Word V -> ( lastS ` ( W ++ (/) ) ) = ( lastS ` W ) )