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	$$⊢W\in \mathrm{Word}V\to \mathrm{lastS}\left(W\mathrm{++}\varnothing \right)=\mathrm{lastS}\left(W\right)$$

Proof

Step	Hyp	Ref	Expression
1		ccatrid	$$⊢W\in \mathrm{Word}V\to W\mathrm{++}\varnothing =W$$
2	1	fveq2d	$$⊢W\in \mathrm{Word}V\to \mathrm{lastS}\left(W\mathrm{++}\varnothing \right)=\mathrm{lastS}\left(W\right)$$