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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 ) )