Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1211 Unicode version

Theorem bnj1211 29146
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1211.1  |-  ( ph  ->  A. x  e.  A  ps )
Assertion
Ref Expression
bnj1211  |-  ( ph  ->  A. x ( x  e.  A  ->  ps ) )

Proof of Theorem bnj1211
StepHypRef Expression
1 bnj1211.1 . 2  |-  ( ph  ->  A. x  e.  A  ps )
2 df-ral 2561 . 2  |-  ( A. x  e.  A  ps  <->  A. x ( x  e.  A  ->  ps )
)
31, 2sylib 188 1  |-  ( ph  ->  A. x ( x  e.  A  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530    e. wcel 1696   A.wral 2556
This theorem is referenced by:  bnj1533  29200  bnj1204  29358  bnj1523  29417
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-ral 2561
  Copyright terms: Public domain W3C validator