Theorem hbe1

Description: The setvar x is not free in E. x ph . Corresponds to the axiom (5) of modal logic (see also modal5 ). (Contributed by NM, 24-Jan-1993)

	Ref	Expression
Assertion	hbe1	|- ( E. x ph -> A. x E. x ph )

Proof

Step	Hyp	Ref	Expression
1		df-ex	|- ( E. x ph <-> -. A. x -. ph )
2		hbn1	|- ( -. A. x -. ph -> A. x -. A. x -. ph )
3	1 2	hbxfrbi	|- ( E. x ph -> A. x E. x ph )