Theorem eldifad

Description: If a class is in the difference of two classes, it is also in the minuend. One-way deduction form of eldif . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	eldifad.1	|- ( ph -> A e. ( B \ C ) )
Assertion	eldifad	|- ( ph -> A e. B )

Proof

Step	Hyp	Ref	Expression
1		eldifad.1	|- ( ph -> A e. ( B \ C ) )
2		eldif	|- ( A e. ( B \ C ) <-> ( A e. B /\ -. A e. C ) )
3	1 2	sylib	|- ( ph -> ( A e. B /\ -. A e. C ) )
4	3	simpld	|- ( ph -> A e. B )