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Theorem prssi 3678
Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015.)
Assertion
Ref Expression
prssi  |-  ( ( A  e.  C  /\  B  e.  C )  ->  { A ,  B }  C_  C )

Proof of Theorem prssi
StepHypRef Expression
1 prssg 3677 . 2  |-  ( ( A  e.  C  /\  B  e.  C )  ->  ( ( A  e.  C  /\  B  e.  C )  <->  { A ,  B }  C_  C
) )
21ibi 175 1  |-  ( ( A  e.  C  /\  B  e.  C )  ->  { A ,  B }  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 1480    C_ wss 3071   {cpr 3528
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534
This theorem is referenced by:  tpssi  3686  prelpwi  4136  onun2  4406  onintexmid  4487  nnregexmid  4534  en2eqpr  6801  m1expcl2  10322  m1expcl  10323  minmax  11008  xrminmax  11041  1idssfct  11803  unopn  12182  bdop  13103  isomninnlem  13255  trilpolemisumle  13261  trilpolemeq1  13263  trilpolemlt1  13264
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