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 Description: Deduction version of nfiota 4343. (Contributed by NM, 18-Feb-2013.)
Hypotheses
Ref Expression
Assertion
Ref Expression

Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 dfiota2 4340 . 2 (℩yψ) = {z y(ψy = z)}
2 nfv 1619 . . . 4 zφ
3 nfiotad.1 . . . . 5 yφ
4 nfiotad.2 . . . . . . 7 (φ → Ⅎxψ)
54adantr 451 . . . . . 6 ((φ ¬ x x = y) → Ⅎxψ)
6 nfcvf 2511 . . . . . . . 8 x x = yxy)
76adantl 452 . . . . . . 7 ((φ ¬ x x = y) → xy)
8 nfcvd 2490 . . . . . . 7 ((φ ¬ x x = y) → xz)
97, 8nfeqd 2503 . . . . . 6 ((φ ¬ x x = y) → Ⅎx y = z)
105, 9nfbid 1832 . . . . 5 ((φ ¬ x x = y) → Ⅎx(ψy = z))
113, 10nfald2 1972 . . . 4 (φ → Ⅎxy(ψy = z))
122, 11nfabd 2508 . . 3 (φx{z y(ψy = z)})
1312nfunid 3898 . 2 (φx{z y(ψy = z)})
141, 13nfcxfrd 2487 1 (φx(℩yψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ wa 358  ∀wal 1540  Ⅎwnf 1544   = wceq 1642  {cab 2339  Ⅎwnfc 2476  ∪cuni 3891  ℩cio 4337 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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by:  nfiota  4343
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