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Mirrors > Home > ILE Home > Th. List > 19.12 | Structured version GIF version |
Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
19.12 | ⊢ (∃x∀yφ → ∀y∃xφ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1416 | . . 3 ⊢ (∀yφ → ∀y∀yφ) | |
2 | 1 | hbex 1511 | . 2 ⊢ (∃x∀yφ → ∀y∃x∀yφ) |
3 | ax-4 1382 | . . 3 ⊢ (∀yφ → φ) | |
4 | 3 | eximi 1475 | . 2 ⊢ (∃x∀yφ → ∃xφ) |
5 | 2, 4 | alrimih 1338 | 1 ⊢ (∃x∀yφ → ∀y∃xφ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1226 ∃wex 1363 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1316 ax-7 1317 ax-gen 1318 ax-ie1 1364 ax-ie2 1365 ax-4 1382 ax-ial 1410 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: hbexd 1567 nfexd 1627 cbvexdh 1784 |
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