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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 1847 | 1 ⊢ (∃𝑥∃𝑦(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜑 ∧ ∃𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∧ wa 398 ∃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 209 df-an 399 df-ex 1780 |
This theorem is referenced by: exdistrv 1955 19.42vv 1957 3exdistr 1961 sbccomlem 3847 coass 6111 uniuni 7477 eulerpartlemgvv 31655 bnj986 32248 dfiota3 33405 ac6s6f 35484 |
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