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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 4747 and pwpw0 4748.) (Contributed by NM, 2-May-2009.) |
Ref | Expression |
---|---|
pwpwpw0 | ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwpr 4834 | 1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∪ cun 3936 ∅c0 4293 𝒫 cpw 4541 {csn 4569 {cpr 4571 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ral 3145 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-pw 4543 df-sn 4570 df-pr 4572 |
This theorem is referenced by: (None) |
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