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Theorem rabssab 4083
Description: A restricted class is a subclass of the corresponding unrestricted class. (Contributed by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
rabssab {𝑥𝐴𝜑} ⊆ {𝑥𝜑}

Proof of Theorem rabssab
StepHypRef Expression
1 df-rab 3431 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 483 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 4063 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 4016 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 394  wcel 2098  {cab 2705  {crab 3430  wss 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-in 3956  df-ss 3966
This theorem is referenced by:  epse  5665  riotasbc  7401  cshwsexa  14814  toponsspwpw  22844  dmtopon  22845  aannenlem2  26284  aalioulem2  26288  ballotlemfmpn  34147  rencldnfilem  42271  rmxyelqirr  42361  rababg  43035
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