Theorem 1p2e3 9245

Description: 1 + 2 = 3 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
1p2e3	|- ( 1 + 2 ) = 3

Proof of Theorem 1p2e3

Step	Hyp	Ref	Expression
1		2cn 9181	. 2 |- 2 e. CC
2		ax-1cn 8092	. 2 |- 1 e. CC
3		2p1e3 9244	. 2 |- ( 2 + 1 ) = 3
4	1, 2, 3	addcomli 8291	1 |- ( 1 + 2 ) = 3

Syntax hints:   = wceq 1395  (class class class)co 6001   1c1 8000   + caddc 8002   2c2 9161   3c3 9162

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8091  ax-1cn 8092  ax-1re 8093  ax-addrcl 8096  ax-addcom 8099

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-2 9169  df-3 9170

This theorem is referenced by:  binom3  10879  3lcm2e6woprm  12608  2exp16  12960  1kp2ke3k  16088