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Theorem rabssab 4041
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 3406 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 485 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 4021 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 3976 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 396  wcel 2106  {cab 2713  {crab 3405  wss 3908
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-in 3915  df-ss 3925
This theorem is referenced by:  epse  5614  riotasbc  7326  cshwsexa  14666  toponsspwpw  22217  dmtopon  22218  aannenlem2  25635  aalioulem2  25639  ballotlemfmpn  32922  rencldnfilem  41046  rmxyelqirr  41136  rababg  41751
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