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Mirrors > Home > MPE Home > Th. List > pwpwpw0 | Structured version Visualization version GIF version |
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4810 and pwpw0 4811.) (Contributed by NM, 2-May-2009.) |
Ref | Expression |
---|---|
pwpwpw0 | ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwpr 4896 | 1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∪ cun 3941 ∅c0 4317 𝒫 cpw 4597 {csn 4623 {cpr 4625 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-ral 3056 df-v 3470 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-pw 4599 df-sn 4624 df-pr 4626 |
This theorem is referenced by: (None) |
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