Theorem nfnae 2442

Description: All variables are effectively bound in a distinct variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2380. Use the weaker nfnaew 2149 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 2441	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	nfn 1856	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Syntax hints:  ¬ wn 3  ∀wal 1535  Ⅎwnf 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2158  ax-12 2178  ax-13 2380

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-nf 1782

This theorem is referenced by:  nfald2  2453  dvelimf  2456  sbequ6  2474  2ax6elem  2478  nfsb4t  2507  sbco2  2519  sbco3  2521  sb9  2527  sbal1  2536  sbal2  2537  nfabd2  2935  ralcom2  3385  dfid3  5596  nfriotad  7416  axextnd  10660  axrepndlem1  10661  axrepndlem2  10662  axrepnd  10663  axunndlem1  10664  axunnd  10665  axpowndlem2  10667  axpowndlem3  10668  axpowndlem4  10669  axpownd  10670  axregndlem2  10672  axregnd  10673  axinfndlem1  10674  axinfnd  10675  axacndlem4  10679  axacndlem5  10680  axacnd  10681  axnulg  35068  axextdist  35763  axextbdist  35764  distel  35767  wl-cbvalnaed  37486  wl-2sb6d  37512  wl-sbalnae  37516  wl-mo2df  37524  wl-mo2tf  37525  wl-eudf  37526  wl-eutf  37527  ax6e2ndeq  44530  ax6e2ndeqVD  44880