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Mirrors > Home > ILE Home > Th. List > vpwex | Unicode version |
Description: Power set axiom: the powerclass of a set is a set. Axiom 4 of [TakeutiZaring] p. 17. (Contributed by NM, 30-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) Revised to prove pwexg 4201 from vpwex 4200. (Revised by BJ, 10-Aug-2022.) |
Ref | Expression |
---|---|
vpwex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pw 3595 |
. 2
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2 | axpow2 4197 |
. . . . 5
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3 | 2 | bm1.3ii 4142 |
. . . 4
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4 | abeq2 2298 |
. . . . 5
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5 | 4 | exbii 1616 |
. . . 4
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6 | 3, 5 | mpbir 146 |
. . 3
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7 | 6 | issetri 2761 |
. 2
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8 | 1, 7 | eqeltri 2262 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 df-in 3150 df-ss 3157 df-pw 3595 |
This theorem is referenced by: pwexg 4201 pwnex 4470 exmidpw2en 6944 istopon 13998 dmtopon 14008 tgdom 14057 |
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