| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > moexexv | Structured version Visualization version GIF version | ||
| Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker moexexvw 2628 when possible. (Contributed by NM, 26-Jan-1997.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| moexexv | ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfv 1914 | . 2 ⊢ Ⅎ𝑦𝜑 | |
| 2 | 1 | moexex 2638 | 1 ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓)) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∀wal 1538 ∃wex 1779 ∃*wmo 2538 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-11 2157 ax-12 2177 ax-13 2377 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-mo 2540 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |