Theorem setind2

Description: Set (epsilon) induction, stated compactly. Given as a homework problem in 1992 by George Boolos (1940-1996). (Contributed by NM, 17-Sep-2003)

	Ref	Expression
Assertion	setind2	|- ( ~P A C_ A -> A = _V )

Proof

Step	Hyp	Ref	Expression
1		pwss	|- ( ~P A C_ A <-> A. x ( x C_ A -> x e. A ) )
2		setind	|- ( A. x ( x C_ A -> x e. A ) -> A = _V )
3	1 2	sylbi	|- ( ~P A C_ A -> A = _V )