Theorem nfnaew 2153

Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae 2456 with a disjoint variable condition, which does not require ax-13 2390. (Contributed by Mario Carneiro, 11-Aug-2016.) (Revised by Gino Giotto, 10-Jan-2024.)

Assertion

Ref	Expression
nfnaew	⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem nfnaew

Step	Hyp	Ref	Expression
1		hbaev 2064	. . 3 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nf5i 2150	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
3	2	nfn 1857	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

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

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:  nfriotadw  7122