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

Theorem nfeu 2220
Description: Bound-variable hypothesis builder for "at most one." Note that x and y needn't be distinct (this makes the proof more difficult). (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
nfeu.1 xφ
Assertion
Ref Expression
nfeu x∃!yφ

Proof of Theorem nfeu
StepHypRef Expression
1 nftru 1554 . . 3 y
2 nfeu.1 . . . 4 xφ
32a1i 10 . . 3 ( ⊤ → Ⅎxφ)
41, 3nfeud 2218 . 2 ( ⊤ → Ⅎx∃!yφ)
54trud 1323 1 x∃!yφ
Colors of variables: wff setvar class
Syntax hints:  wtru 1316  wnf 1544  ∃!weu 2204
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  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208
This theorem is referenced by:  2eu7  2290  2eu8  2291
  Copyright terms: Public domain W3C validator