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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 𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfnae1
StepHypRef Expression
1 wl-nfae1 34319 . 2 𝑥𝑦 𝑦 = 𝑥
21nfn 1838 1 𝑥 ¬ ∀𝑦 𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1520  wnf 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
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