Theorem ex-ss 30815

Description: Example for df-ss 3925. 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 4134	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4599	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3989	1 ⊢ {1, 2} ⊆ {1, 2, 3}

This proof depends on syntax axioms:   ∪ cun 3906   ⊆ wss 3908  {csn 4594  {cpr 4596  {ctp 4598  1c1 11119  2c2 12313  3c3 12314

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-v 3460  df-un 3913  df-ss 3925  df-tp 4599

This theorem is used by:  ex-pss  30816