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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 4705 and pwpw0 4706.) (Contributed by NM, 2-May-2009.) |
Ref | Expression |
---|---|
pwpwpw0 | ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwpr 4794 | 1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 ∪ cun 3879 ∅c0 4243 𝒫 cpw 4497 {csn 4525 {cpr 4527 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-ral 3111 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-pw 4499 df-sn 4526 df-pr 4528 |
This theorem is referenced by: (None) |
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