Theorem wl-nfnae1 34783

Description: Unlike nfnae 2456, this specialized theorem avoids ax-11 2161. (Contributed by Wolf Lammen, 27-Jun-2019.)

Assertion

Ref	Expression
wl-nfnae1	⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfnae1

Step	Hyp	Ref	Expression
1		wl-nfae1 34782	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1857	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Syntax hints:  ¬ wn 3  ∀wal 1535  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-12 2177  ax-13 2390

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1781  df-nf 1785

This theorem is referenced by:  wl-cbvalnaed  34787  wl-2sb6d  34809