Theorem nfae 2433

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2372. (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 2431	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2143	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀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:  nfnae  2434  axc16nfALT  2437  dral2  2438  drex2  2442  drnf2  2444  sbequ5  2465  2ax6elem  2470  sbco3  2513  axbnd  2703  axrepnd  10589  axunnd  10591  axpowndlem3  10594  axpownd  10596  axregndlem1  10597  axregnd  10599  axacndlem1  10602  axacndlem2  10603  axacndlem3  10604  axacndlem4  10605  axacndlem5  10606  axacnd  10607