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

Theorem moani 2334
Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
moani.1  |-  E* x ph
Assertion
Ref Expression
moani  |-  E* x
( ps  /\  ph )

Proof of Theorem moani
StepHypRef Expression
1 moani.1 . 2  |-  E* x ph
2 moan 2333 . 2  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
31, 2ax-mp 5 1  |-  E* x
( ps  /\  ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369   E*wmo 2262
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591  df-eu 2265  df-mo 2266
This theorem is referenced by:  euxfr2  3245  reuxfr2d  4618  fvopab6  5900  1stconst  6766  2ndconst  6767  iunmapdisj  8299  axaddf  9418  axmulf  9419  joinval  15289  meetval  15303  reuxfr3d  26020
  Copyright terms: Public domain W3C validator