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Theorem nfunid 3587
 Description: Deduction version of nfuni 3586. (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 3582 . 2
2 nfv 1421 . . 3
3 nfv 1421 . . . 4
4 nfunid.3 . . . 4
5 nfvd 1422 . . . 4
63, 4, 5nfrexdxy 2357 . . 3
72, 6nfabd 2196 . 2
81, 7nfcxfrd 2176 1
 Colors of variables: wff set class Syntax hints:   wi 4  cab 2026  wnfc 2165  wrex 2307  cuni 3580 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-uni 3581 This theorem is referenced by:  dfnfc2  3598  nfiotadxy  4870
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