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Theorem ssrab3 3721
Description: Subclass relation for a restricted class abstraction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
ssrab3.1 𝐵 = {𝑥𝐴𝜑}
Assertion
Ref Expression
ssrab3 𝐵𝐴
Distinct variable group:   𝑥,𝐴
Allowed substitution hints:   𝜑(𝑥)   𝐵(𝑥)

Proof of Theorem ssrab3
StepHypRef Expression
1 ssrab3.1 . 2 𝐵 = {𝑥𝐴𝜑}
2 ssrab2 3720 . 2 {𝑥𝐴𝜑} ⊆ 𝐴
31, 2eqsstri 3668 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  {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:  usgrres  26245  frgrwopregbsn  27297  frgrwopreg1  27298  eulerpartlemgvv  30566  reprpmtf1o  30832  hgt750lemb  30862  hgt750leme  30864  bnj1212  30996  bnj213  31078  bnj1286  31213  bnj1312  31252  bnj1523  31265
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