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Theorem elssuni 3919
 Description: An element of a class is a subclass of its union. Theorem 8.6 of [Quine] p. 54. Also the basis for Proposition 7.20 of [TakeutiZaring] p. 40. (Contributed by NM, 6-Jun-1994.)
Assertion
Ref Expression
elssuni (A BA B)

Proof of Theorem elssuni
StepHypRef Expression
1 ssid 3290 . 2 A A
2 ssuni 3913 . 2 ((A A A B) → A B)
31, 2mpan 651 1 (A BA B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710   ⊆ wss 3257  ∪cuni 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-uni 3892 This theorem is referenced by:  unissel  3920  ssunieq  3924  ncssfin  6151
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