Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1436 Structured version   Unicode version

Theorem bnj1436 29211
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 2543 . 2  |-  ( x  e.  A  <->  ph )
32biimpi 187 1  |-  ( x  e.  A  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    e. wcel 1725   {cab 2422
This theorem is referenced by:  bnj1517  29221  bnj66  29231  bnj900  29300  bnj1296  29390  bnj1371  29398  bnj1374  29400  bnj1398  29403  bnj1450  29419  bnj1497  29429  bnj1498  29430  bnj1514  29432  bnj1501  29436
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432
  Copyright terms: Public domain W3C validator