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Theorem elpwid 3526
 Description: An element of a power class is a subclass. Deduction form of elpwi 3524. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
elpwid.1 (𝜑𝐴 ∈ 𝒫 𝐵)
Assertion
Ref Expression
elpwid (𝜑𝐴𝐵)

Proof of Theorem elpwid
StepHypRef Expression
1 elpwid.1 . 2 (𝜑𝐴 ∈ 𝒫 𝐵)
2 elpwi 3524 . 2 (𝐴 ∈ 𝒫 𝐵𝐴𝐵)
31, 2syl 14 1 (𝜑𝐴𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1481   ⊆ wss 3076  𝒫 cpw 3515 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082  df-ss 3089  df-pw 3517 This theorem is referenced by:  fopwdom  6738  ssenen  6753  fival  6866  fiuni  6874  elnp1st2nd  7309  ixxssxr  9714  elfzoelz  9956  restid2  12169  epttop  12299  neiss2  12351  blssm  12630  blin2  12641  cncfrss  12771  cncfrss2  12772  pwle2  13367
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