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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 4817 and pwpw0 4818.) (Contributed by NM, 2-May-2009.) |
Ref | Expression |
---|---|
pwpwpw0 | ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwpr 4906 | 1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∪ cun 3961 ∅c0 4339 𝒫 cpw 4605 {csn 4631 {cpr 4633 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-ral 3060 df-v 3480 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-nul 4340 df-pw 4607 df-sn 4632 df-pr 4634 |
This theorem is referenced by: (None) |
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