Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj937 Structured version   Unicode version

Theorem bnj937 32098
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj937.1  |-  ( ph  ->  E. x ps )
Assertion
Ref Expression
bnj937  |-  ( ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem bnj937
StepHypRef Expression
1 bnj937.1 . 2  |-  ( ph  ->  E. x ps )
2 19.9v 1719 . 2  |-  ( E. x ps  <->  ps )
31, 2sylib 196 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  bnj1265  32139  bnj1379  32157  bnj852  32247  bnj1148  32320  bnj1154  32323  bnj1189  32333  bnj1245  32338  bnj1286  32343  bnj1311  32348  bnj1371  32353  bnj1374  32355  bnj1498  32385  bnj1514  32387
  Copyright terms: Public domain W3C validator