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Theorem ssrab3 3829
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 3828 . 2 {𝑥𝐴𝜑} ⊆ 𝐴
31, 2eqsstri 3776 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  {crab 3054  wss 3715
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rab 3059  df-in 3722  df-ss 3729
This theorem is referenced by:  usgrres  26399  frgrwopregbsn  27471  frgrwopreg1  27472  eulerpartlemgvv  30747  reprpmtf1o  31013  hgt750lemb  31043  hgt750leme  31045  bnj1212  31177  bnj213  31259  bnj1286  31394  bnj1312  31433  bnj1523  31446
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