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Theorem rabssab 3723
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 2950 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 476 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 3707 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 3668 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 383  wcel 2030  {cab 2637  {crab 2945  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-in 3614  df-ss 3621
This theorem is referenced by:  epse  5126  riotasbc  6666  toponsspwpw  20774  dmtopon  20775  aannenlem2  24129  aalioulem2  24133  ballotlemfmpn  30684  rencldnfilem  37701  rababg  38196
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