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

Theorem nfmo1 2291
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 2285 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
2 nfe1 1747 . . 3  |-  F/ x E. x ph
3 nfeu1 2290 . . 3  |-  F/ x E! x ph
42, 3nfim 1832 . 2  |-  F/ x
( E. x ph  ->  E! x ph )
51, 4nfxfr 1579 1  |-  F/ x E* x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1550   F/wnf 1553   E!weu 2280   E*wmo 2281
This theorem is referenced by:  moanmo  2340  mopick2  2347  moexex  2349  2eu3  2362  nfrmo1  2871  mob  3108  morex  3110
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554  df-eu 2284  df-mo 2285
  Copyright terms: Public domain W3C validator