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Mirrors > Home > MPE Home > Th. List > 2moexv | Structured version Visualization version GIF version |
Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2moexv | ⊢ (∃*𝑥∃𝑦𝜑 → ∀𝑦∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2147 | . . 3 ⊢ Ⅎ𝑦∃𝑦𝜑 | |
2 | 1 | nfmov 2557 | . 2 ⊢ Ⅎ𝑦∃*𝑥∃𝑦𝜑 |
3 | 19.8a 2178 | . . 3 ⊢ (𝜑 → ∃𝑦𝜑) | |
4 | 3 | moimi 2542 | . 2 ⊢ (∃*𝑥∃𝑦𝜑 → ∃*𝑥𝜑) |
5 | 2, 4 | alrimi 2210 | 1 ⊢ (∃*𝑥∃𝑦𝜑 → ∀𝑦∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 ∃wex 1775 ∃*wmo 2535 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-10 2138 ax-11 2154 ax-12 2174 |
This theorem depends on definitions: df-bi 207 df-or 848 df-tru 1539 df-ex 1776 df-nf 1780 df-mo 2537 |
This theorem is referenced by: 2eu5 2653 |
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