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	⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Proof of Theorem nfnae

Step	Hyp	Ref	Expression
1		nfae 2433	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	nfn 1861	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Syntax hints:  ¬ wn 3  ∀wal 1540  Ⅎwnf 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  34802  axextbdist  34803  distel  34806  wl-cbvalnaed  36449  wl-2sb6d  36471  wl-sbalnae  36475  wl-mo2df  36483  wl-mo2tf  36484  wl-eudf  36485  wl-eutf  36486  ax6e2ndeq  43368  ax6e2ndeqVD  43718