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Theorem abeq1iOLD 2584
Description: Obsolete proof of abeq1i 2583 as of 15-Nov-2019. (Contributed by NM, 31-Jul-1994.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
abeqri.1  |-  { x  |  ph }  =  A
Assertion
Ref Expression
abeq1iOLD  |-  ( ph  <->  x  e.  A )

Proof of Theorem abeq1iOLD
StepHypRef Expression
1 abid 2441 . 2  |-  ( x  e.  { x  | 
ph }  <->  ph )
2 abeqri.1 . . 3  |-  { x  |  ph }  =  A
32eleq2i 2532 . 2  |-  ( x  e.  { x  | 
ph }  <->  x  e.  A )
41, 3bitr3i 251 1  |-  ( ph  <->  x  e.  A )
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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