Theorem ex-ss 28464

Description: Example for df-ss 3870. 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 4072	. 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3})
2		df-tp 4532	. 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3})
3	1, 2	sseqtrri 3924	1 ⊢ {1, 2} ⊆ {1, 2, 3}

Syntax hints:   ∪ cun 3851   ⊆ wss 3853  {csn 4527  {cpr 4529  {ctp 4531  1c1 10695  2c2 11850  3c3 11851

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-v 3400  df-un 3858  df-in 3860  df-ss 3870  df-tp 4532

This theorem is referenced by:  ex-pss  28465