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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 2370. 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 1917 | . 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 396 ∀wal 1539 ∃wex 1781 ∃*wmo 2536 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-10 2137 ax-11 2154 ax-12 2171 ax-13 2370 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-nf 1786 df-mo 2538 |
This theorem is referenced by: (None) |
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