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Mirrors > Home > MPE Home > Th. List > moexexv | Structured version Visualization version GIF version |
Description: "At most one" double quantification. (Contributed by NM, 26-Jan-1997.) |
Ref | Expression |
---|---|
moexexv | ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1992 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | 1 | moexex 2679 | 1 ⊢ ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦∃𝑥(𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∀wal 1630 ∃wex 1853 ∃*wmo 2608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1635 df-ex 1854 df-nf 1859 df-eu 2611 df-mo 2612 |
This theorem is referenced by: mosub 3525 funco 6089 |
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