Theorem 1p2e3 9119

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 9055	. 2 |- 2 e. CC
2		ax-1cn 7967	. 2 |- 1 e. CC
3		2p1e3 9118	. 2 |- ( 2 + 1 ) = 3
4	1, 2, 3	addcomli 8166	1 |- ( 1 + 2 ) = 3

Syntax hints:   = wceq 1364  (class class class)co 5919   1c1 7875   + caddc 7877   2c2 9035   3c3 9036

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175  ax-resscn 7966  ax-1cn 7967  ax-1re 7968  ax-addrcl 7971  ax-addcom 7974

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3160  df-ss 3167  df-2 9043  df-3 9044

This theorem is referenced by:  binom3  10731  3lcm2e6woprm  12227  1kp2ke3k  15286