Metamath Proof Explorer


Theorem eliminable3a

Description: A theorem used to prove the base case of the Eliminability Theorem (see section comment). (Contributed by BJ, 19-Oct-2019) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion eliminable3a
|- ( { x | ph } e. y <-> E. z ( z = { x | ph } /\ z e. y ) )

Proof

Step Hyp Ref Expression
1 dfclel
 |-  ( { x | ph } e. y <-> E. z ( z = { x | ph } /\ z e. y ) )