Theorem sn-negex2

Description: Proof of cnegex2 without ax-mulcom . (Contributed by SN, 5-May-2024)

	Ref	Expression
Assertion	sn-negex2	$$⊢A\in ℂ\to \exists b\in ℂb+A=0$$

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		simpr	$$⊢\left(A+b=0\wedge b+A=0\right)\to b+A=0$$
3	2	reximi	$$⊢\exists b\in ℂ\left(A+b=0\wedge b+A=0\right)\to \exists b\in ℂb+A=0$$
4	1 3	syl	$$⊢A\in ℂ\to \exists b\in ℂb+A=0$$