Theorem nfae 2444

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2379. (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 2442	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2147	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀wal 1536  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 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175  ax-13 2379

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786

This theorem is referenced by:  nfnae  2445  axc16nfALT  2448  dral2  2449  drex2  2453  drnf2  2455  sbequ5  2477  2ax6elem  2482  sbco3  2532  sbalOLD  2551  axbnd  2769  axrepnd  10005  axunnd  10007  axpowndlem3  10010  axpownd  10012  axregndlem1  10013  axregnd  10015  axacndlem1  10018  axacndlem2  10019  axacndlem3  10020  axacndlem4  10021  axacndlem5  10022  axacnd  10023