Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1299 Structured version   Unicode version

Theorem bnj1299 32833
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1299.1  |-  ( ph  ->  E. x  e.  A  ( ps  /\  ch )
)
Assertion
Ref Expression
bnj1299  |-  ( ph  ->  E. x  e.  A  ps )

Proof of Theorem bnj1299
StepHypRef Expression
1 bnj1299.1 . 2  |-  ( ph  ->  E. x  e.  A  ( ps  /\  ch )
)
2 bnj1239 32820 . 2  |-  ( E. x  e.  A  ( ps  /\  ch )  ->  E. x  e.  A  ps )
31, 2syl 16 1  |-  ( ph  ->  E. x  e.  A  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   E.wrex 2810
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-ral 2814  df-rex 2815
This theorem is referenced by:  bnj1497  33072  bnj1498  33073  bnj1501  33079
  Copyright terms: Public domain W3C validator