Theorem sn-negex

Description: Proof of cnegex without ax-mulcom . (Contributed by SN, 30-Apr-2024)

	Ref	Expression
Assertion	sn-negex	$$⊢A\in ℂ\to \exists b\in ℂA+b=0$$

Proof

Step	Hyp	Ref	Expression
1		sn-negex12	$$⊢A\in ℂ\to \exists b\in ℂ\left(A+b=0\wedge b+A=0\right)$$
2		simpl	$$⊢\left(A+b=0\wedge b+A=0\right)\to A+b=0$$
3	2	reximi	$$⊢\exists b\in ℂ\left(A+b=0\wedge b+A=0\right)\to \exists b\in ℂA+b=0$$
4	1 3	syl	$$⊢A\in ℂ\to \exists b\in ℂA+b=0$$