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Theorem naev 2061
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
naev (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑢 𝑢 = 𝑣)
Distinct variable group:   𝑣,𝑢

Proof of Theorem naev
StepHypRef Expression
1 aev 2058 . 2 (∀𝑢 𝑢 = 𝑣 → ∀𝑥 𝑥 = 𝑦)
21con3i 154 1 (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑢 𝑢 = 𝑣)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1780
This theorem is referenced by:  naev2  2062  wl-sbcom2d-lem2  35756  wl-sbal1  35759  wl-sbal2  35760  wl-ax11-lem3  35779
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