MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.2 Unicode version

Theorem 19.2 1672
Description: Theorem 19.2 of [Margaris] p. 89. Note: This proof is very different from Margaris' because we only have Tarski's FOL axiom schemes available at this point. See the later 19.2g 1782 for a more conventional proof. (Contributed by NM, 2-Aug-2017.)
Assertion
Ref Expression
19.2  |-  ( A. x ph  ->  E. x ph )

Proof of Theorem 19.2
StepHypRef Expression
1 equid 1645 . . 3  |-  x  =  x
21notnoti 115 . . . 4  |-  -.  -.  x  =  x
32spfalw 1671 . . 3  |-  ( A. x  -.  x  =  x  ->  -.  x  =  x )
41, 3mt2 170 . 2  |-  -.  A. x  -.  x  =  x
5 idd 21 . . 3  |-  ( x  =  x  ->  ( ph  ->  ph ) )
65speimfw 1626 . 2  |-  ( -. 
A. x  -.  x  =  x  ->  ( A. x ph  ->  E. x ph ) )
74, 6ax-mp 8 1  |-  ( A. x ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  19.39  1673  19.24  1674  19.34  1675  eusv2i  4530  extt  24253  pm10.251  26966  a9e2eq  27606  a9e2eqVD  27963
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529
  Copyright terms: Public domain W3C validator