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Theorem nfeqf1 2374
Description: An equation between setvar is free of any other setvar. Usage of this theorem is discouraged because it depends on ax-13 2367. (Contributed by Wolf Lammen, 10-Jun-2019.) (New usage is discouraged.)
Assertion
Ref Expression
nfeqf1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦 = 𝑧)
Distinct variable group:   𝑥,𝑧

Proof of Theorem nfeqf1
StepHypRef Expression
1 nfeqf2 2372 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑧 = 𝑦)
2 equcom 2014 . . 3 (𝑧 = 𝑦𝑦 = 𝑧)
32nfbii 1847 . 2 (Ⅎ𝑥 𝑧 = 𝑦 ↔ Ⅎ𝑥 𝑦 = 𝑧)
41, 3sylib 217 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦 = 𝑧)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1532  wnf 1778
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-13 2367
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-nf 1779
This theorem is referenced by:  dveeq1  2375  sbal2  2524  nfmod2  2548  nfiotad  6505  wl-mo2df  37037  wl-eudf  37039
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