Theorem ralrid

Description: Sufficient condition for the restricted universal quantifier. Deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	ralrid.1	|- ( ph -> A. x ( x e. A -> ps ) )
Assertion	ralrid	|- ( ph -> A. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ralrid.1	|- ( ph -> A. x ( x e. A -> ps ) )
2		df-ral	|- ( A. x e. A ps <-> A. x ( x e. A -> ps ) )
3	1 2	sylibr	|- ( ph -> A. x e. A ps )