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	$$⊢\neg \phi \to \forall x\neg \phi$$
Assertion	spnfw	$$⊢\forall x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		spnfw.1	$$⊢\neg \phi \to \forall x\neg \phi$$
2		idd	$$⊢x=y\to \left(\phi \to \phi \right)$$
3	1 2	spimw	$$⊢\forall x\phi \to \phi$$