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Theorem snsspr1 3503
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.)
Assertion
Ref Expression
snsspr1 {A} ⊆ {A, B}

Proof of Theorem snsspr1
StepHypRef Expression
1 ssun1 3100 . 2 {A} ⊆ ({A} ∪ {B})
2 df-pr 3374 . 2 {A, B} = ({A} ∪ {B})
31, 2sseqtr4i 2972 1 {A} ⊆ {A, B}
Colors of variables: wff set class
Syntax hints:  cun 2909  wss 2911  {csn 3367  {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-pr 3374
This theorem is referenced by:  snsstp1  3505  ssprr  3518  uniop  3983  op1stb  4175  op1stbg  4176  ltrelxr  6857
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