Theorem bj-nfnnfTEMP

Description: New nonfreeness is equivalent to old nonfreeness on core FOL axioms plus sp . (Contributed by BJ, 28-Jul-2023) The proof should not rely on df-nf except via df-nf directly. (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-nfnnfTEMP	|- ( F// x ph <-> F/ x ph )

Proof

Step	Hyp	Ref	Expression
1		bj-dfnnf3	|- ( F// x ph <-> ( E. x ph -> A. x ph ) )
2		df-nf	|- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
3	1 2	bitr4i	|- ( F// x ph <-> F/ x ph )