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Theorem prssi 3750
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 3749 . 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 3129  {cpr 3593
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 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599
This theorem is referenced by:  prssd  3751  tpssi  3759  prelpwi  4214  onun2  4489  onintexmid  4572  nnregexmid  4620  en2eqpr  6906  m1expcl2  10541  m1expcl  10542  minmax  11237  xrminmax  11272  1idssfct  12114  subrgin  13363  unopn  13475  bdop  14597  012of  14715  isomninnlem  14748  trilpolemisumle  14756  trilpolemeq1  14758  trilpolemlt1  14759  iswomninnlem  14767  iswomni0  14769  ismkvnnlem  14770  nconstwlpolemgt0  14781
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