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Theorem prssi 3603
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 3602 . 2 ((𝐴𝐶𝐵𝐶) → ((𝐴𝐶𝐵𝐶) ↔ {𝐴, 𝐵} ⊆ 𝐶))
21ibi 175 1 ((𝐴𝐶𝐵𝐶) → {𝐴, 𝐵} ⊆ 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wcel 1439  wss 3002  {cpr 3453
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 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-un 3006  df-in 3008  df-ss 3015  df-sn 3458  df-pr 3459
This theorem is referenced by:  tpssi  3611  prelpwi  4052  onun2  4322  onintexmid  4403  nnregexmid  4449  en2eqpr  6679  m1expcl2  10040  m1expcl  10041  minmax  10724  1idssfct  11438  unopn  11767  bdop  12070
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