Theorem nfnae 2432

Description: All variables are effectively bound in a distinct variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2370. Use the weaker nfnaew 2150 when possible. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.)

Assertion

Ref	Expression
nfnae	⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Proof of Theorem nfnae

Step	Hyp	Ref	Expression
1		nfae 2431	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	nfn 1857	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Syntax hints:  ¬ wn 3  ∀wal 1538  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-11 2158  ax-12 2178  ax-13 2370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784

This theorem is referenced by:  nfald2  2443  dvelimf  2446  sbequ6  2464  2ax6elem  2468  nfsb4t  2497  sbco2  2509  sbco3  2511  sb9  2517  sbal1  2526  sbal2  2527  nfabd2  2915  ralcom2  3348  dfid3  5529  nfriotad  7337  axextnd  10520  axrepndlem1  10521  axrepndlem2  10522  axrepnd  10523  axunndlem1  10524  axunnd  10525  axpowndlem2  10527  axpowndlem3  10528  axpowndlem4  10529  axpownd  10530  axregndlem2  10532  axregnd  10533  axinfndlem1  10534  axinfnd  10535  axacndlem4  10539  axacndlem5  10540  axacnd  10541  axnulg  35075  axextdist  35780  axextbdist  35781  distel  35784  wl-cbvalnaed  37513  wl-2sb6d  37539  wl-sbalnae  37543  wl-mo2df  37551  wl-mo2tf  37552  wl-eudf  37553  wl-eutf  37554  ax6e2ndeq  44542  ax6e2ndeqVD  44891