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Theorem rabssab 4044
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 3407 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 486 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 4024 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 3979 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 397  wcel 2107  {cab 2710  {crab 3406  wss 3911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3446  df-in 3918  df-ss 3928
This theorem is referenced by:  epse  5617  riotasbc  7333  cshwsexa  14718  toponsspwpw  22287  dmtopon  22288  aannenlem2  25705  aalioulem2  25709  ballotlemfmpn  33151  rencldnfilem  41186  rmxyelqirr  41276  rababg  41934
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