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Theorem wl-naev 33432
 Description: If some set variables can assume different values, then any two distinct set variables cannot always be the same. (Contributed by Wolf Lammen, 10-Aug-2019.)
Assertion
Ref Expression
wl-naev (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑢 𝑢 = 𝑣)
Distinct variable group:   𝑣,𝑢

Proof of Theorem wl-naev
StepHypRef Expression
1 aev 2025 . 2 (∀𝑢 𝑢 = 𝑣 → ∀𝑥 𝑥 = 𝑦)
21con3i 150 1 (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑢 𝑢 = 𝑣)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1521 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745 This theorem is referenced by:  wl-sbcom2d-lem2  33473  wl-sbal1  33476  wl-sbal2  33477  wl-ax11-lem3  33494
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