Theorem ex-ss 30522

Description: Example for df-ss 3907. 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 4114	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4567	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3971	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3888   ⊆ wss 3890  {csn 4562  {cpr 4564  {ctp 4566  1c1 11037  2c2 12234  3c3 12235

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-un 3895  df-ss 3907  df-tp 4567

This theorem is referenced by:  ex-pss  30523