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Theorem ssrab3 3241
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 3240 . 2 {𝑥𝐴𝜑} ⊆ 𝐴
31, 2eqsstri 3187 1 𝐵𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1353  {crab 2459  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rab 2464  df-in 3135  df-ss 3142
This theorem is referenced by:  pcprecl  12259  pcprendvds  12260  lgsfcl2  14040
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