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Mirrors > Home > MPE Home > Th. List > 2moex | Structured version Visualization version GIF version |
Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2moex | ⊢ (∃*𝑥∃𝑦𝜑 → ∀𝑦∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2122 | . . 3 ⊢ Ⅎ𝑦∃𝑦𝜑 | |
2 | 1 | nfmo 2604 | . 2 ⊢ Ⅎ𝑦∃*𝑥∃𝑦𝜑 |
3 | 19.8a 2146 | . . 3 ⊢ (𝜑 → ∃𝑦𝜑) | |
4 | 3 | moimi 2583 | . 2 ⊢ (∃*𝑥∃𝑦𝜑 → ∃*𝑥𝜑) |
5 | 2, 4 | alrimi 2180 | 1 ⊢ (∃*𝑥∃𝑦𝜑 → ∀𝑦∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1523 ∃wex 1765 ∃*wmo 2576 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1781 ax-4 1795 ax-5 1892 ax-6 1951 ax-7 1996 ax-10 2114 ax-11 2128 ax-12 2143 ax-13 2346 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-tru 1528 df-ex 1766 df-nf 1770 df-mo 2578 |
This theorem is referenced by: 2eu2 2710 2eu5OLD 2715 |
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