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Theorem nfnae 2434
Description: All variables are effectively bound in a distinct variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2372. Use the weaker nfnaew 2146 when possible. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.)
Assertion
Ref Expression
nfnae 𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Proof of Theorem nfnae
StepHypRef Expression
1 nfae 2433 . 2 𝑧𝑥 𝑥 = 𝑦
21nfn 1861 1 𝑧 ¬ ∀𝑥 𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1540  wnf 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-11 2155  ax-12 2172  ax-13 2372
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787
This theorem is referenced by:  nfald2  2445  dvelimf  2448  sbequ6  2466  2ax6elem  2470  nfsb4t  2499  sbco2  2511  sbco3  2513  sb9  2519  sbal1  2528  sbal2  2529  nfabd2  2930  ralcom2  3374  dfid3  5578  nfriotad  7377  axextnd  10586  axrepndlem1  10587  axrepndlem2  10588  axrepnd  10589  axunndlem1  10590  axunnd  10591  axpowndlem2  10593  axpowndlem3  10594  axpowndlem4  10595  axpownd  10596  axregndlem2  10598  axregnd  10599  axinfndlem1  10600  axinfnd  10601  axacndlem4  10605  axacndlem5  10606  axacnd  10607  axextdist  34771  axextbdist  34772  distel  34775  wl-cbvalnaed  36401  wl-2sb6d  36423  wl-sbalnae  36427  wl-mo2df  36435  wl-mo2tf  36436  wl-eudf  36437  wl-eutf  36438  ax6e2ndeq  43320  ax6e2ndeqVD  43670
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