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Theorem prssi 3751
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 3750 . 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 2148  wss 3130  {cpr 3594
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-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-un 3134  df-in 3136  df-ss 3143  df-sn 3599  df-pr 3600
This theorem is referenced by:  prssd  3752  tpssi  3760  prelpwi  4215  onun2  4490  onintexmid  4573  nnregexmid  4621  en2eqpr  6907  m1expcl2  10542  m1expcl  10543  minmax  11238  xrminmax  11273  1idssfct  12115  subrgin  13365  unopn  13508  bdop  14630  012of  14748  isomninnlem  14781  trilpolemisumle  14789  trilpolemeq1  14791  trilpolemlt1  14792  iswomninnlem  14800  iswomni0  14802  ismkvnnlem  14803  nconstwlpolemgt0  14814
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