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Mirrors > Home > MPE Home > Th. List > hbaev | Structured version Visualization version GIF version |
Description: Version of hbae 2445 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2054. (Contributed by Wolf Lammen, 22-Mar-2021.) |
Ref | Expression |
---|---|
hbaev | ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aev2 2054 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 |
This theorem is referenced by: nfnaew 2144 euae 2740 wl-moae 34638 |
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