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Theorem abeq2iOLD 2582
Description: Obsolete proof of abeq2i 2581 as of 15-Nov-2019. (Contributed by NM, 3-Apr-1996.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
abeqi.1  |-  A  =  { x  |  ph }
Assertion
Ref Expression
abeq2iOLD  |-  ( x  e.  A  <->  ph )

Proof of Theorem abeq2iOLD
StepHypRef Expression
1 abeqi.1 . . 3  |-  A  =  { x  |  ph }
21eleq2i 2532 . 2  |-  ( x  e.  A  <->  x  e.  { x  |  ph }
)
3 abid 2441 . 2  |-  ( x  e.  { x  | 
ph }  <->  ph )
42, 3bitri 249 1  |-  ( x  e.  A  <->  ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    = wceq 1370    e. wcel 1758   {cab 2439
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449
This theorem is referenced by: (None)
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