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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-hbae1 | Structured version Visualization version GIF version |
Description: This specialization of hbae 2432 does not depend on ax-11 2153. (Contributed by Wolf Lammen, 8-Aug-2021.) |
Ref | Expression |
---|---|
wl-hbae1 | ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11n 2427 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥) | |
2 | axc11n 2427 | . . 3 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦) | |
3 | 2 | axc4i 2319 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑦∀𝑥 𝑥 = 𝑦) |
4 | 1, 3 | syl 17 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1963 ax-7 2003 ax-10 2137 ax-12 2173 ax-13 2373 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-ex 1775 df-nf 1779 |
This theorem is referenced by: (None) |
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