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Theorem elpwid 3396
 Description: An element of a power class is a subclass. Deduction form of elpwi 3395. (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 3395 . 2 (𝐴 ∈ 𝒫 𝐵𝐴𝐵)
31, 2syl 14 1 (𝜑𝐴𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1409   ⊆ wss 2944  𝒫 cpw 3386 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2951  df-ss 2958  df-pw 3388 This theorem is referenced by:  fopwdom  6340  elnp1st2nd  6631  ixxssxr  8869  elfzoelz  9105
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