Theorem nfae 2436

Description: All variables are effectively bound in an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2375. (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 2434	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2144	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀wal 1535  Ⅎwnf 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175  ax-13 2375

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781

This theorem is referenced by:  nfnae  2437  axc16nfALT  2440  dral2  2441  drex2  2445  drnf2  2447  sbequ5  2468  2ax6elem  2473  sbco3  2516  axbnd  2705  axrepnd  10632  axunnd  10634  axpowndlem3  10637  axpownd  10639  axregndlem1  10640  axregnd  10642  axacndlem1  10645  axacndlem2  10646  axacndlem3  10647  axacndlem4  10648  axacndlem5  10649  axacnd  10650