Theorem ex-ss 27284

Description: Example for df-ss 3588. 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 3776	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4182	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtr4i 3638	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3572   ⊆ wss 3574  {csn 4177  {cpr 4179  {ctp 4181  1c1 9937  2c2 11070  3c3 11071

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-in 3581  df-ss 3588  df-tp 4182

This theorem is referenced by:  ex-pss  27285