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

Theorem moan 2290
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )

Proof of Theorem moan
StepHypRef Expression
1 simpr 448 . 2  |-  ( ( ps  /\  ph )  ->  ph )
21moimi 2286 1  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   E*wmo 2240
This theorem is referenced by:  moani  2291  mooran1  2293  mormo  2864  rmoan  3076
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