MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfmo1 Structured version   Unicode version

Theorem nfmo1 2299
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfmo1  |-  F/ x E* x ph

Proof of Theorem nfmo1
StepHypRef Expression
1 df-mo 2293 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1750 . . 3  |-  F/ x E. x ph
3 nfeu1 2298 . . 3  |-  F/ x E! x ph
42, 3nfim 1835 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1580 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1551   F/wnf 1554   E!weu 2288   E*wmo 2289
This theorem is referenced by:  moanmo  2348  mopick2  2355  moexex  2357  2eu3  2370  nfrmo1  2886  mob  3125  morex  3127
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555  df-eu 2292  df-mo 2293
  Copyright terms: Public domain W3C validator