Theorem ex-ss 30413

Description: Example for df-ss 3948. 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 4158	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4611	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 4013	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3929   ⊆ wss 3931  {csn 4606  {cpr 4608  {ctp 4610  1c1 11135  2c2 12300  3c3 12301

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466  df-un 3936  df-ss 3948  df-tp 4611

This theorem is referenced by:  ex-pss  30414