Theorem setinds2

Description: _E induction schema, using implicit substitution. (Contributed by Scott Fenton, 10-Mar-2011)

	Ref	Expression
Hypotheses	setinds2.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	setinds2.2	$$⊢\forall y\in x\psi \to \phi$$
Assertion	setinds2	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		setinds2.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		setinds2.2	$$⊢\forall y\in x\psi \to \phi$$
3		nfv	$$⊢Ⅎx\psi$$
4	3 1 2	setinds2f	$$⊢\phi$$