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 Description: A pair of elements of a class is a subset of the class. Theorem 7.5 of [Quine] p. 49. (Contributed by NM, 30-May-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Hypotheses
Ref Expression
Assertion
Ref Expression

StepHypRef Expression
1 unss 3216 . 2
2 prss.1 . . . 4
32snss 3615 . . 3
4 prss.2 . . . 4
54snss 3615 . . 3
63, 5anbi12i 453 . 2
7 df-pr 3500 . . 3
87sseq1i 3089 . 2
91, 6, 83bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wcel 1463  cvv 2657   cun 3035   wss 3037  csn 3493  cpr 3494 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-v 2659  df-un 3041  df-in 3043  df-ss 3050  df-sn 3499  df-pr 3500 This theorem is referenced by:  tpss  3651  prsspw  3658  exmidpw  6755
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