Theorem ex-ss 31058

Description: Example for df-ss 3901. 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 4179	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4593	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3962	1 ⊢ {1, 2} ⊆ {1, 2, 3}

This proof depends on syntax axioms:   ⊆ wss 3900   ∪ cun 4152  {csn 4588  {cpr 4590  {ctp 4592  1c1 11228  2c2 12424  3c3 12425

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-tp 4593

This theorem is used by:  ex-pss  31059