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Mirrors > Home > MPE Home > Th. List > pw0 | Structured version Unicode version |
Description: Compute the power set of the empty set. Theorem 89 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
pw0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3778 |
. . 3
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2 | 1 | abbii 2588 |
. 2
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3 | df-pw 3973 |
. 2
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4 | df-sn 3989 |
. 2
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5 | 2, 3, 4 | 3eqtr4i 2493 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-v 3080 df-dif 3442 df-in 3446 df-ss 3453 df-nul 3749 df-pw 3973 df-sn 3989 |
This theorem is referenced by: p0ex 4590 pwfi 7720 ackbij1lem14 8516 fin1a2lem12 8694 0tsk 9036 hashbc 12327 incexclem 13420 sn0topon 18737 sn0cld 18829 ust0 19929 uhgra0v 23416 usgra0v 23462 esumnul 26667 rankeq1o 28373 ssoninhaus 28458 |
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