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Metamath Proof Explorer

Theorem s1dmALT

Description: Alternate version of s1dm , having a shorter proof, but requiring that A is a set. (Contributed by AV, 9-Jan-2020) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	s1dmALT	$⊢ A \in S \to dom ⟨“ A ”⟩ = \{0\}$

Proof

Step	Hyp	Ref	Expression
1		s1val	$⊢ A \in S \to ⟨“ A ”⟩ = \{⟨0, A⟩\}$
2	1	dmeqd	$⊢ A \in S \to dom ⟨“ A ”⟩ = dom \{⟨0, A⟩\}$
3		dmsnopg	$⊢ A \in S \to dom \{⟨0, A⟩\} = \{0\}$
4	2 3	eqtrd	$⊢ A \in S \to dom ⟨“ A ”⟩ = \{0\}$