Theorem exintr

Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993) (Proof shortened by BJ, 16-Sep-2022)

	Ref	Expression
Assertion	exintr	|- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ( ph /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		ancl	|- ( ( ph -> ps ) -> ( ph -> ( ph /\ ps ) ) )
2	1	aleximi	|- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ( ph /\ ps ) ) )