Theorem bj-nnfe1

Description: See nfe1 . (Contributed by BJ, 12-Aug-2023) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-nnfe1	|- F// x E. x ph

Proof

Step	Hyp	Ref	Expression
1		bj-modal4e	|- ( E. x E. x ph -> E. x ph )
2		hbe1	|- ( E. x ph -> A. x E. x ph )
3		df-bj-nnf	|- ( F// x E. x ph <-> ( ( E. x E. x ph -> E. x ph ) /\ ( E. x ph -> A. x E. x ph ) ) )
4	1 2 3	mpbir2an	|- F// x E. x ph