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Theorem nfnaew 2151
Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae 2448 with a disjoint variable condition, which does not require ax-13 2382. (Contributed by Mario Carneiro, 11-Aug-2016.) (Revised by Gino Giotto, 10-Jan-2024.)
Assertion
Ref Expression
nfnaew 𝑧 ¬ ∀𝑥 𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem nfnaew
StepHypRef Expression
1 hbaev 2064 . . 3 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
21nf5i 2148 . 2 𝑧𝑥 𝑥 = 𝑦
32nfn 1858 1 𝑧 ¬ ∀𝑥 𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1536  wnf 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 2143
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786
This theorem is referenced by:  nfriotadw  7105
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