Theorem sucunisn

Description: The successor to the union of any singleton of a set is the successor of the set. (Contributed by RP, 11-Feb-2025)

	Ref	Expression
Assertion	sucunisn	$$⊢A\in V\to \mathrm{suc}\bigcup \left\{A\right\}=\mathrm{suc}A$$

Proof

Step	Hyp	Ref	Expression
1		unisng	$$⊢A\in V\to \bigcup \left\{A\right\}=A$$
2		suceq	$$⊢\bigcup \left\{A\right\}=A\to \mathrm{suc}\bigcup \left\{A\right\}=\mathrm{suc}A$$
3	1 2	syl	$$⊢A\in V\to \mathrm{suc}\bigcup \left\{A\right\}=\mathrm{suc}A$$