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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 1958. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
exdistr | ⊢ (∃𝑥∃𝑦(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜑 ∧ ∃𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.42v 1956 | . 2 ⊢ (∃𝑦(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃𝑦𝜓)) | |
2 | 1 | exbii 1849 | 1 ⊢ (∃𝑥∃𝑦(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜑 ∧ ∃𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 395 ∃wex 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1781 |
This theorem is referenced by: exdistrv 1958 19.42vv 1960 3exdistr 1963 rexcom4 3284 sbccomlem 3864 coass 6264 uniuni 7753 eulerpartlemgvv 33840 bnj986 34431 dfiota3 35366 ac6s6f 37507 |
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