Theorem wl-nfnae1 34320

Description: Unlike nfnae 2413, this specialized theorem avoids ax-11 2126. (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 34319	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1838	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Syntax hints:  ¬ wn 3  ∀wal 1520  Ⅎwnf 1765

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-10 2112  ax-12 2141  ax-13 2344

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-ex 1762  df-nf 1766

This theorem is referenced by:  wl-cbvalnaed  34323  wl-2sb6d  34344