MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  2moex Unicode version

Theorem 2moex 2310
Description: Double quantification with "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex  |-  ( E* x E. y ph  ->  A. y E* x ph )

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 1739 . . 3  |-  F/ y E. y ph
21nfmo 2256 . 2  |-  F/ y E* x E. y ph
3 19.8a 1754 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2286 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1773 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546   E.wex 1547   E*wmo 2240
This theorem is referenced by:  2eu2  2320  2eu5  2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244
  Copyright terms: Public domain W3C validator