Theorem bj-nnfa1

Description: See nfa1 . (Contributed by BJ, 12-Aug-2023) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-nnfa1	|- F// x A. x ph

Proof

Step	Hyp	Ref	Expression
1		hbe1a	|- ( E. x A. x ph -> A. x ph )
2		bj-modal4	|- ( A. x ph -> A. x A. x ph )
3		df-bj-nnf	|- ( F// x A. x ph <-> ( ( E. x A. x ph -> A. x ph ) /\ ( A. x ph -> A. x A. x ph ) ) )
4	1 2 3	mpbir2an	|- F// x A. x ph