Theorem sbcex

Description: By our definition of proper substitution, it can only be true if the substituted expression is a set. (Contributed by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Assertion	sbcex	|- ( [. A / x ]. ph -> A e. _V )

Proof

Step	Hyp	Ref	Expression
1		df-sbc	|- ( [. A / x ]. ph <-> A e. { x | ph } )
2		elex	|- ( A e. { x | ph } -> A e. _V )
3	1 2	sylbi	|- ( [. A / x ]. ph -> A e. _V )