Theorem r19.29OLD

Description: Obsolete version of r19.29 as of 22-Dec-2024. (Contributed by NM, 31-Aug-1999) (Proof shortened by Andrew Salmon, 30-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	r19.29OLD	|- ( ( A. x e. A ph /\ E. x e. A ps ) -> E. x e. A ( ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.2	|- ( ph -> ( ps -> ( ph /\ ps ) ) )
2	1	ralimi	|- ( A. x e. A ph -> A. x e. A ( ps -> ( ph /\ ps ) ) )
3		rexim	|- ( A. x e. A ( ps -> ( ph /\ ps ) ) -> ( E. x e. A ps -> E. x e. A ( ph /\ ps ) ) )
4	2 3	syl	|- ( A. x e. A ph -> ( E. x e. A ps -> E. x e. A ( ph /\ ps ) ) )
5	4	imp	|- ( ( A. x e. A ph /\ E. x e. A ps ) -> E. x e. A ( ph /\ ps ) )