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Theorem nfmod2 2217
 Description: Bound-variable hypothesis builder for uniqueness. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfeud2.1 yφ
nfeud2.2 ((φ ¬ x x = y) → Ⅎxψ)
Assertion
Ref Expression
nfmod2 (φ → Ⅎx∃*yψ)

Proof of Theorem nfmod2
StepHypRef Expression
1 df-mo 2209 . 2 (∃*yψ ↔ (yψ∃!yψ))
2 nfeud2.1 . . . 4 yφ
3 nfeud2.2 . . . 4 ((φ ¬ x x = y) → Ⅎxψ)
42, 3nfexd2 1973 . . 3 (φ → Ⅎxyψ)
52, 3nfeud2 2216 . . 3 (φ → Ⅎx∃!yψ)
64, 5nfimd 1808 . 2 (φ → Ⅎx(yψ∃!yψ))
71, 6nfxfrd 1571 1 (φ → Ⅎx∃*yψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  ∀wal 1540  ∃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  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  df-mo 2209 This theorem is referenced by:  nfmod  2219  nfrmod  2784  nfrmo  2786
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