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Theorem nfnid 4681
Description: A setvar variable is not free from itself. The proof relies on dtru 4643, that is, it is not true in a one-element domain. (Contributed by Mario Carneiro, 8-Oct-2016.)
Assertion
Ref Expression
nfnid

Proof of Theorem nfnid
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dtru 4643 . . 3
2 ax-ext 2435 . . . . 5
32sps 1865 . . . 4
43alimi 1633 . . 3
51, 4mto 176 . 2
6 df-nfc 2607 . . 3
7 sbnf2 2183 . . . . 5
8 elsb4 2179 . . . . . . 7
9 elsb4 2179 . . . . . . 7
108, 9bibi12i 315 . . . . . 6
11102albii 1641 . . . . 5
127, 11bitri 249 . . . 4
1312albii 1640 . . 3
14 alrot3 1846 . . 3
156, 13, 143bitri 271 . 2
165, 15mtbir 299 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739  F/_wnfc 2605
This theorem is referenced by:  nfcvb  4682
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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581  ax-pow 4630
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-nfc 2607
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