Theorem abssdv

Description: Deduction of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006)

	Ref	Expression
Hypothesis	abssdv.1	|- ( ph -> ( ps -> x e. A ) )
Assertion	abssdv	|- ( ph -> { x | ps } C_ A )

Proof

Step	Hyp	Ref	Expression
1		abssdv.1	|- ( ph -> ( ps -> x e. A ) )
2	1	alrimiv	|- ( ph -> A. x ( ps -> x e. A ) )
3		abss	|- ( { x | ps } C_ A <-> A. x ( ps -> x e. A ) )
4	2 3	sylibr	|- ( ph -> { x | ps } C_ A )