Theorem eliminable3b 32845

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.)

Assertion

Ref	Expression
eliminable3b	|- ( { x | ph } e. { y | ps } <-> E. z ( z = { x | ph } /\ z e. { y | ps } ) )

Distinct variable groups:   x, z   y, z   ph, z   ps, z

Allowed substitution hints:   ph( x, y)   ps( x, y)

Proof of Theorem eliminable3b

Step	Hyp	Ref	Expression
1		df-clel 2618	1 |- ( { x | ph } e. { y | ps } <-> E. z ( z = { x | ph } /\ z e. { y | ps } ) )

Syntax hints:   <-> wb 196   /\ wa 384   = wceq 1483   E.wex 1704   e. wcel 1990   {cab 2608

This theorem depends on definitions:  df-clel 2618

This theorem is referenced by: (None)