Theorem sn-negex2

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

	Ref	Expression
Assertion	sn-negex2	|- ( A e. CC -> E. b e. CC ( b + A ) = 0 )

Proof

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