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Metamath Proof Explorer

Theorem s2cl

Description: A doubleton word is a word. (Contributed by Stefan O'Rear, 23-Aug-2015) (Revised by Mario Carneiro, 26-Feb-2016)

		Ref	Expression
	Assertion	s2cl	$⊢ (A \in X \land B \in X) \to ⟨“ A B ”⟩ \in Word X$

Step	Hyp	Ref	Expression
1		simpl	$⊢ (A \in X \land B \in X) \to A \in X$
2		simpr	$⊢ (A \in X \land B \in X) \to B \in X$
3	1 2	s2cld	$⊢ (A \in X \land B \in X) \to ⟨“ A B ”⟩ \in Word X$