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Theorem nfeqf1 2399
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 2396 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑧 = 𝑦)
2 equcom 2115 . . 3 (𝑧 = 𝑦𝑦 = 𝑧)
32nfbii 1947 . 2 (Ⅎ𝑥 𝑧 = 𝑦 ↔ Ⅎ𝑥 𝑦 = 𝑧)
41, 3sylib 209 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑦 = 𝑧)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1650  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-10 2183  ax-13 2352
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875  df-nf 1879
This theorem is referenced by:  dveeq1  2400  sbal2  2553  nfmod2  2577  nfeud2OLD  2613  nfiotad  6034  wl-mo2df  33709  wl-eudf  33711
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