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Theorem nfeqf1 2298
 Description: An equation between setvar is free of any other setvar. (Contributed by Wolf Lammen, 10-Jun-2019.)
Assertion
Ref Expression
nfeqf1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦 = 𝑧)
Distinct variable group:   𝑥,𝑧

Proof of Theorem nfeqf1
StepHypRef Expression
1 nfeqf2 2296 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑧 = 𝑦)
2 equcom 1944 . . 3 (𝑧 = 𝑦𝑦 = 𝑧)
32nfbii 1777 . 2 (Ⅎ𝑥 𝑧 = 𝑦 ↔ Ⅎ𝑥 𝑦 = 𝑧)
41, 3sylib 208 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦 = 𝑧)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1480  Ⅎwnf 1707 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-10 2018  ax-12 2046  ax-13 2245 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1704  df-nf 1709 This theorem is referenced by:  dveeq1  2299  sbal2  2460  nfeud2  2481  nfiotad  5852  wl-mo2df  33332  wl-eudf  33334
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