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Theorem nfnid 4393
 Description: A set variable is not free from itself. The proof relies on dtru 4390, 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 4390 . . 3
2 ax-ext 2417 . . . . 5
32sps 1770 . . . 4
43alimi 1568 . . 3
51, 4mto 169 . 2
6 df-nfc 2561 . . 3
7 sbnf2 2184 . . . . 5
8 elsb4 2180 . . . . . . 7
9 elsb4 2180 . . . . . . 7
108, 9bibi12i 307 . . . . . 6
11102albii 1576 . . . . 5
127, 11bitri 241 . . . 4
1312albii 1575 . . 3
14 alrot3 1753 . . 3
156, 13, 143bitri 263 . 2
165, 15mtbir 291 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177  wal 1549  wnf 1553  wsb 1658  wnfc 2559 This theorem is referenced by:  nfcvb  4394 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4338  ax-pow 4377 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-nfc 2561
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