Theorem ex-ss 28791

Description: Example for df-ss 3904. 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

Step	Hyp	Ref	Expression
1		ssun1 4106	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4566	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3958	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3885   ⊆ wss 3887  {csn 4561  {cpr 4563  {ctp 4565  1c1 10872  2c2 12028  3c3 12029

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-un 3892  df-in 3894  df-ss 3904  df-tp 4566

This theorem is referenced by:  ex-pss  28792