Theorem bnj1211

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1211.1	|- ( ph -> A. x e. A ps )
Assertion	bnj1211	|- ( ph -> A. x ( x e. A -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1211.1	|- ( ph -> A. x e. A ps )
2		df-ral	|- ( A. x e. A ps <-> A. x ( x e. A -> ps ) )
3	1 2	sylib	|- ( ph -> A. x ( x e. A -> ps ) )