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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 2453 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2063. (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 2063 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 |
This theorem is referenced by: nfnaew 2153 euae 2745 wl-moae 34771 |
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