MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exanOLD Unicode version

Theorem exanOLD 1904
Description: Obsolete proof of exan 1903 as of 13-Jan-2018. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
exan.1  |-  ( E. x ph  /\  ps )
Assertion
Ref Expression
exanOLD  |-  E. x
( ph  /\  ps )

Proof of Theorem exanOLD
StepHypRef Expression
1 nfe1 1747 . . . 4  |-  F/ x E. x ph
2119.28 1842 . . 3  |-  ( A. x ( E. x ph  /\  ps )  <->  ( E. x ph  /\  A. x ps ) )
3 exan.1 . . 3  |-  ( E. x ph  /\  ps )
42, 3mpgbi 1558 . 2  |-  ( E. x ph  /\  A. x ps )
5 19.29r 1607 . 2  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ph  /\  ps ) )
64, 5ax-mp 8 1  |-  E. x
( ph  /\  ps )
Colors of variables: wff set class
Syntax hints:    /\ wa 359   A.wal 1549   E.wex 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
  Copyright terms: Public domain W3C validator