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Theorem sspwi 4576
Description: The powerclass preserves inclusion (inference form). (Contributed by BJ, 13-Apr-2024.)
Hypothesis
Ref Expression
sspwi.1 𝐴𝐵
Assertion
Ref Expression
sspwi 𝒫 𝐴 ⊆ 𝒫 𝐵

Proof of Theorem sspwi
StepHypRef Expression
1 sspwi.1 . 2 𝐴𝐵
2 sspw 4575 . 2 (𝐴𝐵 → 𝒫 𝐴 ⊆ 𝒫 𝐵)
31, 2ax-mp 5 1 𝒫 𝐴 ⊆ 𝒫 𝐵
Colors of variables: wff setvar class
Syntax hints:  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:  pwunss  4582  pwundif  4588  pwdom  9079  wdompwdom  9522  rankxplim  9823  hashbclem  14358  incexclem  15729  sscpwex  17706  wunfunc  17793  wunfuncOLD  17794  tsmsres  23518  cfilresi  24682  vitali  25000  sqff1o  26554  ldgenpisyslem1  32826  imambfm  32926  ballotlem2  33152  dssmapnvod  42384  gneispace  42498  sge0less  44723
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