Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1196 Structured version   Unicode version

Theorem bnj1196 32090
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1196.1  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
bnj1196  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )

Proof of Theorem bnj1196
StepHypRef Expression
1 bnj1196.1 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 df-rex 2801 . 2  |-  ( E. x  e.  A  ps  <->  E. x ( x  e.  A  /\  ps )
)
31, 2sylib 196 1  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   E.wex 1587    e. wcel 1758   E.wrex 2796
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-rex 2801
This theorem is referenced by:  bnj1209  32092  bnj1265  32108  bnj1379  32126  bnj1521  32146  bnj900  32224  bnj986  32249  bnj1189  32302  bnj1245  32307  bnj1286  32312  bnj1311  32317  bnj1450  32343  bnj1498  32354
  Copyright terms: Public domain W3C validator