ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  1p2e3 Unicode version

Theorem 1p2e3 8822
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
StepHypRef Expression
1 2cn 8759 . 2  |-  2  e.  CC
2 ax-1cn 7681 . 2  |-  1  e.  CC
3 2p1e3 8821 . 2  |-  ( 2  +  1 )  =  3
41, 2, 3addcomli 7875 1  |-  ( 1  +  2 )  =  3
Colors of variables: wff set class
Syntax hints:    = wceq 1316  (class class class)co 5742   1c1 7589    + caddc 7591   2c2 8739   3c3 8740
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-resscn 7680  ax-1cn 7681  ax-1re 7682  ax-addrcl 7685  ax-addcom 7688
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054  df-2 8747  df-3 8748
This theorem is referenced by:  binom3  10377  3lcm2e6woprm  11694  1kp2ke3k  12863
  Copyright terms: Public domain W3C validator