Theorem bj-nnfnfTEMP

Description: New nonfreeness implies old nonfreeness on minimal implicational calculus (the proof indicates it uses ax-3 because of set.mm's definition of the biconditional, but the proof actually holds in minimal implicational calculus). (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-nnfnfTEMP	|- ( F// x ph -> F/ x ph )

Proof

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