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Theorem sspwd 4577
Description: The powerclass preserves inclusion (deduction form). (Contributed by BJ, 13-Apr-2024.)
Hypothesis
Ref Expression
sspwd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
sspwd (𝜑 → 𝒫 𝐴 ⊆ 𝒫 𝐵)

Proof of Theorem sspwd
StepHypRef Expression
1 sspwd.1 . 2 (𝜑𝐴𝐵)
2 sspw 4575 . 2 (𝐴𝐵 → 𝒫 𝐴 ⊆ 𝒫 𝐵)
31, 2syl 17 1 (𝜑 → 𝒫 𝐴 ⊆ 𝒫 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3914  𝒫 cpw 4564
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3449  df-in 3921  df-ss 3931  df-pw 4566
This theorem is referenced by:  pweq  4578  pwel  5340  marypha1lem  9377  pwwf  9751  rankpwi  9767  ackbij2lem1  10163  fictb  10189  ssfin2  10264  ssfin3ds  10274  ttukeylem2  10454  hashbcss  16884  isacs1i  17545  mreacs  17546  acsfn  17547  isacs3lem  18439  isacs5lem  18442  tgcmp  22775  imastopn  23094  fgabs  23253  fgtr  23264  trfg  23265  ssufl  23292  alexsubb  23420  cfiluweak  23670  cmetss  24703  minveclem4a  24817  minveclem4  24819  madess  27235  ldsysgenld  32823  neibastop1  34884  neibastop2lem  34885  neibastop2  34886  sstotbnd2  36283  prjcrv0  41018  isnacs3  41080  aomclem2  41429  sge0iunmptlemre  44746
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