Theorem ex-ss 26676

Description: Example for df-ss 3554. 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 3738	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4130	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtr4i 3601	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3538   ⊆ wss 3540  {csn 4125  {cpr 4127  {ctp 4129  1c1 9816  2c2 10947  3c3 10948

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-tp 4130

This theorem is referenced by:  ex-pss  26677