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 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 𝐶 B 𝐶) → {A, B} ⊆ 𝐶)

StepHypRef Expression
1 prssg 3512 . 2 ((A 𝐶 B 𝐶) → ((A 𝐶 B 𝐶) ↔ {A, B} ⊆ 𝐶))
21ibi 165 1 ((A 𝐶 B 𝐶) → {A, B} ⊆ 𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ wcel 1390   ⊆ wss 2911  {cpr 3368 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374 This theorem is referenced by:  tpssi  3521  prelpwi  3941  onun2  4182  nnregexmid  4285  m1expcl2  8911  m1expcl  8912  bdop  9310
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