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Theorem nfeqf1 2444
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 2442 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥 𝑧 = 𝑦)
2 equcom 2100 . . 3 (𝑧 = 𝑦𝑦 = 𝑧)
32nfbii 1927 . 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 1630  wnf 1857
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859
This theorem is referenced by:  dveeq1  2445  sbal2  2598  nfeud2  2619  nfiotad  6015  wl-mo2df  33665  wl-eudf  33667
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