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  10522  axrepndlem1  10523  axrepndlem2  10524  axrepnd  10525  axunndlem1  10526  axunnd  10527  axpowndlem2  10529  axpowndlem3  10530  axpowndlem4  10531  axpownd  10532  axregndlem2  10534  axregnd  10535  axinfndlem1  10536  axinfnd  10537  axacndlem4  10541  axacndlem5  10542  axacnd  10543  axnulg  35076  axextdist  35781  axextbdist  35782  distel  35785  wl-cbvalnaed  37514  wl-2sb6d  37540  wl-sbalnae  37544  wl-mo2df  37552  wl-mo2tf  37553  wl-eudf  37554  wl-eutf  37555  ax6e2ndeq  44543  ax6e2ndeqVD  44892