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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  Ⅎwnf 1544  ∃!weu 2204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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
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