Theorem spimvw

Description: A weak form of specialization. Lemma 8 of KalishMontague p. 87. Uses only Tarski's FOL axiom schemes. For stronger forms using more axioms, see spimv and spimfv . (Contributed by NM, 9-Apr-2017)

	Ref	Expression
Hypothesis	spimvw.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	spimvw	$$⊢\forall x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		spimvw.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2		ax-5	$$⊢\neg \psi \to \forall x\neg \psi$$
3	2 1	spimw	$$⊢\forall x\phi \to \psi$$