Theorem ralim

Description: Distribution of restricted quantification over implication. (Contributed by NM, 9-Feb-1997) (Proof shortened by Wolf Lammen, 1-Dec-2019)

	Ref	Expression
Assertion	ralim	|- ( A. x e. A ( ph -> ps ) -> ( A. x e. A ph -> A. x e. A ps ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	ral2imi	|- ( A. x e. A ( ph -> ps ) -> ( A. x e. A ph -> A. x e. A ps ) )