Theorem ex-ss 31033

Description: Example for df-ss 3896. 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 4176	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4589	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3957	1 ⊢ {1, 2} ⊆ {1, 2, 3}

This proof depends on syntax axioms:   ⊆ wss 3895   ∪ cun 4149  {csn 4584  {cpr 4586  {ctp 4588  1c1 11204  2c2 12400  3c3 12401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-un 4151  df-tp 4589

This theorem is used by:  ex-pss  31034