Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1521 Structured version   Unicode version

Theorem bnj1521 29491
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1521.1  |-  ( ch 
->  E. x  e.  B  ph )
bnj1521.2  |-  ( th  <->  ( ch  /\  x  e.  B  /\  ph )
)
bnj1521.3  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
bnj1521  |-  ( ch 
->  E. x th )

Proof of Theorem bnj1521
StepHypRef Expression
1 bnj1521.1 . . 3  |-  ( ch 
->  E. x  e.  B  ph )
21bnj1196 29435 . 2  |-  ( ch 
->  E. x ( x  e.  B  /\  ph ) )
3 bnj1521.2 . 2  |-  ( th  <->  ( ch  /\  x  e.  B  /\  ph )
)
4 bnj1521.3 . 2  |-  ( ch 
->  A. x ch )
52, 3, 4bnj1345 29465 1  |-  ( ch 
->  E. x th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ w3a 982   A.wal 1435   E.wex 1659    e. wcel 1867   E.wrex 2774
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-ex 1660  df-nf 1664  df-rex 2779
This theorem is referenced by:  bnj1204  29650  bnj1311  29662  bnj1398  29672  bnj1408  29674  bnj1450  29688  bnj1312  29696  bnj1501  29705  bnj1523  29709
  Copyright terms: Public domain W3C validator