Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elpwi Structured version   GIF version

Theorem elpwi 3360
 Description: Subset relation implied by membership in a power class. (Contributed by NM, 17-Feb-2007.)
Assertion
Ref Expression
elpwi (A 𝒫 BAB)

Proof of Theorem elpwi
StepHypRef Expression
1 elpwg 3359 . 2 (A 𝒫 B → (A 𝒫 BAB))
21ibi 165 1 (A 𝒫 BAB)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1390   ⊆ wss 2911  𝒫 cpw 3351 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353 This theorem is referenced by:  elpwid  3361  elelpwi  3362  elpw2g  3901  eldifpw  4174  iunpw  4177  f1opw2  5648
 Copyright terms: Public domain W3C validator