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Mirrors > Home > ILE Home > Th. List > pwex | GIF version |
Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993.) |
Ref | Expression |
---|---|
pwex.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
pwex | ⊢ 𝒫 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwex.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | pwexg 4180 | . 2 ⊢ (𝐴 ∈ V → 𝒫 𝐴 ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝒫 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 Vcvv 2737 𝒫 cpw 3575 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-pw 3577 |
This theorem is referenced by: p0ex 4188 pp0ex 4189 ord3ex 4190 abexssex 6125 fnpm 6655 exmidpw 6907 pw1on 7224 pw1dom2 7225 pw1nel3 7229 sucpw1ne3 7230 sucpw1nel3 7231 npex 7471 axcnex 7857 pnfxr 8009 mnfxr 8013 ixxex 9898 istopon 13449 dmtopon 13459 fncld 13534 |
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