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Theorem wl-naev 32973
 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 1980 . 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 1478 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932 This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702 This theorem is referenced by:  wl-sbcom2d-lem2  33014  wl-sbal1  33017  wl-sbal2  33018  wl-ax11-lem3  33035
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