Theorem bnj946

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

	Ref	Expression
Hypothesis	bnj946.1	|- ( ph <-> A. x e. A ps )
Assertion	bnj946	|- ( ph <-> A. x ( x e. A -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bnj946.1	|- ( ph <-> A. x e. A ps )
2		df-ral	|- ( A. x e. A ps <-> A. x ( x e. A -> ps ) )
3	1 2	bitri	|- ( ph <-> A. x ( x e. A -> ps ) )