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Theorem ex-ss 29413
Description: Example for df-ss 3932. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-ss {1, 2} ⊆ {1, 2, 3}

Proof of Theorem ex-ss
StepHypRef Expression
1 ssun1 4137 . 2 {1, 2} ⊆ ({1, 2} ∪ {3})
2 df-tp 4596 . 2 {1, 2, 3} = ({1, 2} ∪ {3})
31, 2sseqtrri 3986 1 {1, 2} ⊆ {1, 2, 3}
Colors of variables: wff setvar class
Syntax hints:  cun 3913  wss 3915  {csn 4591  {cpr 4593  {ctp 4595  1c1 11059  2c2 12215  3c3 12216
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-un 3920  df-in 3922  df-ss 3932  df-tp 4596
This theorem is referenced by:  ex-pss  29414
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