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Theorem bnj1436 29188
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1436.1  |-  A  =  { x  |  ph }
Assertion
Ref Expression
bnj1436  |-  ( x  e.  A  ->  ph )

Proof of Theorem bnj1436
StepHypRef Expression
1 bnj1436.1 . . 3  |-  A  =  { x  |  ph }
21abeq2i 2403 . 2  |-  ( x  e.  A  <->  ph )
32biimpi 186 1  |-  ( x  e.  A  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    e. wcel 1696   {cab 2282
This theorem is referenced by:  bnj1517  29198  bnj66  29208  bnj900  29277  bnj1296  29367  bnj1371  29375  bnj1374  29377  bnj1398  29380  bnj1450  29396  bnj1497  29406  bnj1498  29407  bnj1514  29409  bnj1501  29413
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292
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