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Theorem nfnid 4629
 Description: A setvar variable is not free from itself. The proof relies on dtru 4594, 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 4594 . . 3
2 ax-ext 2431 . . . . 5
32sps 1943 . . . 4
43alimi 1684 . . 3
51, 4mto 180 . 2
6 df-nfc 2581 . . 3
7 sbnf2 2268 . . . . 5
8 elsb4 2264 . . . . . . 7
9 elsb4 2264 . . . . . . 7
108, 9bibi12i 317 . . . . . 6
11102albii 1692 . . . . 5
127, 11bitri 253 . . . 4
1312albii 1691 . . 3
14 alrot3 1924 . . 3
156, 13, 143bitri 275 . 2
165, 15mtbir 301 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 188  wal 1442  wnf 1667  wsb 1797  wnfc 2579 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-8 1889  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-nul 4534  ax-pow 4581 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-nfc 2581 This theorem is referenced by:  nfcvb  4630
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