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Theorem abeq2iOLD 2585
Description: Obsolete proof of abeq2i 2584 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 2535 . 2  |-  ( x  e.  A  <->  x  e.  { x  |  ph }
)
3 abid 2444 . 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 1395    e. wcel 1819   {cab 2442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-12 1855  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452
This theorem is referenced by: (None)
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