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 ∈ 𝑉 → suc ∪ { 𝐴 } = suc 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		unisng	⊢ ( 𝐴 ∈ 𝑉 → ∪ { 𝐴 } = 𝐴 )
2		suceq	⊢ ( ∪ { 𝐴 } = 𝐴 → suc ∪ { 𝐴 } = suc 𝐴 )
3	1 2	syl	⊢ ( 𝐴 ∈ 𝑉 → suc ∪ { 𝐴 } = suc 𝐴 )