Theorem sn-negex

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

	Ref	Expression
Assertion	sn-negex	|- ( A e. CC -> E. b e. CC ( A + b ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		sn-negex12	|- ( A e. CC -> E. b e. CC ( ( A + b ) = 0 /\ ( b + A ) = 0 ) )
2		simpl	|- ( ( ( A + b ) = 0 /\ ( b + A ) = 0 ) -> ( A + b ) = 0 )
3	2	reximi	|- ( E. b e. CC ( ( A + b ) = 0 /\ ( b + A ) = 0 ) -> E. b e. CC ( A + b ) = 0 )
4	1 3	syl	|- ( A e. CC -> E. b e. CC ( A + b ) = 0 )