Theorem nfae 2349

Description: All variables are effectively bound in an identical variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfae	⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Proof of Theorem nfae

Step	Hyp	Ref	Expression
1		hbae 2348	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2064	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀wal 1521  Ⅎwnf 1748

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750

This theorem is referenced by:  nfnae  2351  axc16nfALT  2354  dral2  2355  drnf2  2361  sbequ5  2415  sbco3  2445  2ax6elem  2477  sbal  2490  exists1  2590  axi12  2629  axrepnd  9454  axunnd  9456  axpowndlem3  9459  axpownd  9461  axregndlem1  9462  axregnd  9464  axacndlem1  9467  axacndlem2  9468  axacndlem3  9469  axacndlem4  9470  axacndlem5  9471  axacnd  9472