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Mirrors > Home > MPE Home > Th. List > naev | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
naev | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑢 𝑢 = 𝑣) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aev 2058 | . 2 ⊢ (∀𝑢 𝑢 = 𝑣 → ∀𝑥 𝑥 = 𝑦) | |
2 | 1 | con3i 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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