Theorem spnfw

Description: Weak version of sp . Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017) (Proof shortened by Wolf Lammen, 13-Aug-2017)

	Ref	Expression
Hypothesis	spnfw.1	|- ( -. ph -> A. x -. ph )
Assertion	spnfw	|- ( A. x ph -> ph )

Proof

Step	Hyp	Ref	Expression
1		spnfw.1	|- ( -. ph -> A. x -. ph )
2		idd	|- ( x = y -> ( ph -> ph ) )
3	1 2	spimw	|- ( A. x ph -> ph )