Theorem nfae 2431

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2370. (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 2429	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2147	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀wal 1538  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-11 2158  ax-12 2178  ax-13 2370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784

This theorem is referenced by:  nfnae  2432  axc16nfALT  2435  dral2  2436  drex2  2440  drnf2  2442  sbequ5  2463  2ax6elem  2468  sbco3  2511  axbnd  2700  axrepnd  10488  axunnd  10490  axpowndlem3  10493  axpownd  10495  axregndlem1  10496  axregnd  10498  axacndlem1  10501  axacndlem2  10502  axacndlem3  10503  axacndlem4  10504  axacndlem5  10505  axacnd  10506