Theorem tfis2

Description: Transfinite Induction Schema, using implicit substitution. (Contributed by NM, 18-Aug-1994)

	Ref	Expression
Hypotheses	tfis2.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	tfis2.2	$$⊢x\in \mathrm{On}\to \left(\forall y\in x\psi \to \phi \right)$$
Assertion	tfis2	$$⊢x\in \mathrm{On}\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		tfis2.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		tfis2.2	$$⊢x\in \mathrm{On}\to \left(\forall y\in x\psi \to \phi \right)$$
3		nfv	$$⊢Ⅎx\psi$$
4	3 1 2	tfis2f	$$⊢x\in \mathrm{On}\to \phi$$