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Mirrors > Home > ILE Home > Th. List > axpow2 | Unicode version |
Description: A variant of the Axiom of Power Sets ax-pow 3927 using subset notation. Problem in {BellMachover] p. 466. (Contributed by NM, 4-Jun-2006.) |
Ref | Expression |
---|---|
axpow2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-pow 3927 | . 2 | |
2 | dfss2 2934 | . . . . 5 | |
3 | 2 | imbi1i 227 | . . . 4 |
4 | 3 | albii 1359 | . . 3 |
5 | 4 | exbii 1496 | . 2 |
6 | 1, 5 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wex 1381 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-pow 3927 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 |
This theorem is referenced by: axpow3 3930 pwex 3932 |
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