Theorem 2reureurex

Description: Double restricted existential uniqueness implies restricted existential uniqueness with restricted existence. (Contributed by AV, 5-Jul-2023)

	Ref	Expression
Assertion	2reureurex	|- ( E! x e. A , y e. B ph -> E! x e. A E. y e. B ph )

Proof

Step	Hyp	Ref	Expression
1		df-2reu	|- ( E! x e. A , y e. B ph <-> ( E! x e. A E. y e. B ph /\ E! y e. B E. x e. A ph ) )
2	1	simplbi	|- ( E! x e. A , y e. B ph -> E! x e. A E. y e. B ph )