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| Mirrors > Home > MPE Home > Th. List > exdistr | Structured version Visualization version GIF version | ||
| Description: Distribution of existential quantifiers. See also exdistrv 1955. (Contributed by NM, 9-Mar-1995.) |
| Ref | Expression |
|---|---|
| exdistr | ⊢ (∃𝑥∃𝑦(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜑 ∧ ∃𝑦𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.42v 1953 | . 2 ⊢ (∃𝑦(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃𝑦𝜓)) | |
| 2 | 1 | exbii 1848 | 1 ⊢ (∃𝑥∃𝑦(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜑 ∧ ∃𝑦𝜓)) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ∧ wa 395 ∃wex 1779 |
| 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 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 |
| This theorem is referenced by: exdistrv 1955 19.42vv 1957 3exdistr 1960 rexcom4 3288 sbccomlemOLD 3870 coass 6285 uniuni 7782 eulerpartlemgvv 34378 bnj986 34969 dfiota3 35924 ac6s6f 38180 |
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