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Theorem bj-nfeel2 33114
 Description: Non-freeness in an equality. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nfeel2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦𝑧)
Distinct variable group:   𝑥,𝑧

Proof of Theorem bj-nfeel2
Dummy variable 𝑡 is distinct from all other variables.
StepHypRef Expression
1 nfv 1980 . 2 𝑥 𝑡𝑧
2 elequ1 2134 . 2 (𝑡 = 𝑦 → (𝑡𝑧𝑦𝑧))
31, 2bj-dvelimv 33113 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦𝑧)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1618  Ⅎwnf 1845 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-8 2129  ax-10 2156  ax-11 2171  ax-12 2184  ax-13 2379 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1623  df-ex 1842  df-nf 1847 This theorem is referenced by:  bj-axc14nf  33115
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