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Theorem rabssab 3652
 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 2905 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 476 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 3637 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 3598 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 383   ∈ wcel 1977  {cab 2596  {crab 2900   ⊆ wss 3540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-in 3547  df-ss 3554 This theorem is referenced by:  epse  5021  riotasbc  6526  aannenlem2  23888  aalioulem2  23892  ballotlemfmpn  29883  bj-toponss  32241  bj-dmtopon  32242  rencldnfilem  36402  rababg  36898
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