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Theorem rabssab 4095
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 3434 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 484 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 4077 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 4030 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 395  wcel 2106  {cab 2712  {crab 3433  wss 3963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-rab 3434  df-ss 3980
This theorem is referenced by:  epse  5671  riotasbc  7406  cshwsexa  14859  toponsspwpw  22944  dmtopon  22945  aannenlem2  26386  aalioulem2  26390  ballotlemfmpn  34476  rencldnfilem  42808  rmxyelqirr  42898  rababg  43564
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