Theorem wfis2g

Description: Well-Ordered Induction Schema, using implicit substitution. (Contributed by Scott Fenton, 11-Feb-2011)

	Ref	Expression
Hypotheses	wfis2g.1	$$⊢y=z\to \left(\phi \leftrightarrow \psi \right)$$
	wfis2g.2	$$⊢y\in A\to \left(\forall z\in Pred\left(R,A,y\right)\psi \to \phi \right)$$
Assertion	wfis2g	$$⊢\left(R\mathrm{We}A\wedge R\mathrm{Se}A\right)\to \forall y\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		wfis2g.1	$$⊢y=z\to \left(\phi \leftrightarrow \psi \right)$$
2		wfis2g.2	$$⊢y\in A\to \left(\forall z\in Pred\left(R,A,y\right)\psi \to \phi \right)$$
3		nfv	$$⊢Ⅎy\psi$$
4	3 1 2	wfis2fg	$$⊢\left(R\mathrm{We}A\wedge R\mathrm{Se}A\right)\to \forall y\in A\phi$$