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Mirrors > Home > MPE Home > Th. List > hbaev | Structured version Visualization version GIF version |
Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2426 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2054. (Contributed by NM, 13-May-1993.) (Revised 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 1532 |
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 1964 ax-7 2004 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1775 |
This theorem is referenced by: nfnaewOLD 2139 dral1v 2362 euae 2651 wl-moae 36983 |
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