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Theorem prssi 3791
Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015.)
Assertion
Ref Expression
prssi ((𝐴𝐶𝐵𝐶) → {𝐴, 𝐵} ⊆ 𝐶)

Proof of Theorem prssi
StepHypRef Expression
1 prssg 3790 . 2 ((𝐴𝐶𝐵𝐶) → ((𝐴𝐶𝐵𝐶) ↔ {𝐴, 𝐵} ⊆ 𝐶))
21ibi 176 1 ((𝐴𝐶𝐵𝐶) → {𝐴, 𝐵} ⊆ 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wcel 2176  wss 3166  {cpr 3634
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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187
This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-pr 3640
This theorem is referenced by:  prssd  3792  tpssi  3800  prelpwi  4258  onun2  4538  onintexmid  4621  nnregexmid  4669  rex2dom  6910  en2eqpr  7004  m1expcl2  10706  m1expcl  10707  minmax  11541  xrminmax  11576  1idssfct  12437  subrngin  13975  subrgin  14006  lssincl  14147  unopn  14477  bdop  15811  012of  15930  isomninnlem  15969  trilpolemisumle  15977  trilpolemeq1  15979  trilpolemlt1  15980  iswomninnlem  15988  iswomni0  15990  ismkvnnlem  15991  nconstwlpolemgt0  16003
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