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 2153 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 1864	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Syntax hints:  ¬ wn 3  ∀wal 1540  Ⅎwnf 1790

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-10 2145  ax-11 2162  ax-12 2179  ax-13 2372

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-nf 1791

This theorem is referenced by:  nfald2  2445  dvelimf  2448  sbequ6  2466  2ax6elem  2470  nfsb4t  2503  sbco2  2515  sbco3  2517  sb9  2523  sbal1  2533  sbal2  2534  nfabd2  2925  ralcom2  3266  dfid3  5431  nfriotad  7139  axextnd  10091  axrepndlem1  10092  axrepndlem2  10093  axrepnd  10094  axunndlem1  10095  axunnd  10096  axpowndlem2  10098  axpowndlem3  10099  axpowndlem4  10100  axpownd  10101  axregndlem2  10103  axregnd  10104  axinfndlem1  10105  axinfnd  10106  axacndlem4  10110  axacndlem5  10111  axacnd  10112  axextdist  33347  axextbdist  33348  distel  33351  wl-cbvalnaed  35314  wl-2sb6d  35336  wl-sbalnae  35340  wl-mo2df  35348  wl-mo2tf  35349  wl-eudf  35350  wl-eutf  35351  ax6e2ndeq  41717  ax6e2ndeqVD  42067