Theorem nfae 2432

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2371. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.)

Assertion

Ref	Expression
nfae	⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Proof of Theorem nfae

Step	Hyp	Ref	Expression
1		hbae 2430	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2142	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀wal 1539  Ⅎwnf 1785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-11 2154  ax-12 2171  ax-13 2371

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-nf 1786

This theorem is referenced by:  nfnae  2433  axc16nfALT  2436  dral2  2437  drex2  2441  drnf2  2443  sbequ5  2464  2ax6elem  2469  sbco3  2512  axbnd  2702  axrepnd  10591  axunnd  10593  axpowndlem3  10596  axpownd  10598  axregndlem1  10599  axregnd  10601  axacndlem1  10604  axacndlem2  10605  axacndlem3  10606  axacndlem4  10607  axacndlem5  10608  axacnd  10609