Theorem setinds2

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

	Ref	Expression
Hypotheses	setinds2.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
	setinds2.2	⊢ ( ∀ 𝑦 ∈ 𝑥 𝜓 → 𝜑 )
Assertion	setinds2	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		setinds2.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		setinds2.2	⊢ ( ∀ 𝑦 ∈ 𝑥 𝜓 → 𝜑 )
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	3 1 2	setinds2f	⊢ 𝜑