New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfmo1 GIF version

Theorem nfmo1 2215
 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 x∃*xφ

Proof of Theorem nfmo1
StepHypRef Expression
1 df-mo 2209 . 2 (∃*xφ ↔ (xφ∃!xφ))
2 nfe1 1732 . . 3 xxφ
3 nfeu1 2214 . . 3 x∃!xφ
42, 3nfim 1813 . 2 x(xφ∃!xφ)
51, 4nfxfr 1570 1 x∃*xφ
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541  Ⅎwnf 1544  ∃!weu 2204  ∃*wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209 This theorem is referenced by:  moanmo  2264  mopick2  2271  moexex  2273  2eu3  2286  nfrmo1  2782  mob  3018  morex  3020
 Copyright terms: Public domain W3C validator