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  3340  dfid3  5517  nfriotad  7317  axextnd  10485  axrepndlem1  10486  axrepndlem2  10487  axrepnd  10488  axunndlem1  10489  axunnd  10490  axpowndlem2  10492  axpowndlem3  10493  axpowndlem4  10494  axpownd  10495  axregndlem2  10497  axregnd  10498  axinfndlem1  10499  axinfnd  10500  axacndlem4  10504  axacndlem5  10505  axacnd  10506  axnulg  35075  axextdist  35793  axextbdist  35794  distel  35797  wl-cbvalnaed  37526  wl-2sb6d  37552  wl-sbalnae  37556  wl-mo2df  37564  wl-mo2tf  37565  wl-eudf  37566  wl-eutf  37567  ax6e2ndeq  44553  ax6e2ndeqVD  44902