Theorem alseueu

Description: "The ph is ps " implies that exactly one thing is both ph and ps . This is the half of dfalseu2 that drops the universal conjunct; it does not reverse, so E! x ( ph /\ ps ) cannot be used in place of an "all some one" statement. (Contributed by David A. Wheeler, 21-Jul-2026)

	Ref	Expression
Assertion	alseueu	|- ( AE! x ( ph -> ps ) -> E! x ( ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		dfalseu2	|- ( AE! x ( ph -> ps ) <-> ( A. x ( ph -> ps ) /\ E! x ( ph /\ ps ) ) )
2	1	simprbi	|- ( AE! x ( ph -> ps ) -> E! x ( ph /\ ps ) )