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Metamath Proof Explorer

Theorem sucdifsn2

Description: Absorption of union with a singleton by difference. (Contributed by Peter Mazsa, 24-Jul-2024)

		Ref	Expression
	Assertion	sucdifsn2	$⊢ (A \cup \{A\}) ∖ \{A\} = A$

Step	Hyp	Ref	Expression
1		disjcsn	$⊢ A \cap \{A\} = \emptyset$
2		undif5	$⊢ A \cap \{A\} = \emptyset \to (A \cup \{A\}) ∖ \{A\} = A$
3	1 2	ax-mp	$⊢ (A \cup \{A\}) ∖ \{A\} = A$