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Theorem nfunid 3898
 Description: Deduction version of nfuni 3897. (Contributed by NM, 18-Feb-2013.)
Hypothesis
Ref Expression
nfunid.3 (φxA)
Assertion
Ref Expression
nfunid (φxA)

Proof of Theorem nfunid
Dummy variables y z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 3893 . 2 A = {y z A y z}
2 nfv 1619 . . 3 yφ
3 nfv 1619 . . . 4 zφ
4 nfunid.3 . . . 4 (φxA)
5 nfvd 1620 . . . 4 (φ → Ⅎx y z)
63, 4, 5nfrexd 2666 . . 3 (φ → Ⅎxz A y z)
72, 6nfabd 2508 . 2 (φx{y z A y z})
81, 7nfcxfrd 2487 1 (φxA)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476  ∃wrex 2615  ∪cuni 3891 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-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-uni 3892 This theorem is referenced by:  dfnfc2  3909  nfiotad  4342
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