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Theorem rabssab 3215
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 2444 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 simpr 109 . . 3 ((𝑥𝐴𝜑) → 𝜑)
32ss2abi 3200 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ {𝑥𝜑}
41, 3eqsstri 3160 1 {𝑥𝐴𝜑} ⊆ {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  wa 103  wcel 2128  {cab 2143  {crab 2439  wss 3102
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rab 2444  df-in 3108  df-ss 3115
This theorem is referenced by:  epse  4302  riotasbc  5795  genipv  7429  toponsspwpwg  12431  dmtopon  12432
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