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Theorem nfunid 4256
Description: Deduction version of nfuni 4255. (Contributed by NM, 18-Feb-2013.)
Hypothesis
Ref Expression
nfunid.3
Assertion
Ref Expression
nfunid

Proof of Theorem nfunid
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 4251 . 2
2 nfv 1707 . . 3
3 nfv 1707 . . . 4
4 nfunid.3 . . . 4
5 nfvd 1708 . . . 4
63, 4, 5nfrexd 2919 . . 3
72, 6nfabd 2641 . 2
81, 7nfcxfrd 2618 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  {cab 2442  F/_wnfc 2605  E.wrex 2808  U.cuni 4249
This theorem is referenced by:  dfnfc2  4267  nfiotad  5559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-uni 4250
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